Description
It explains the Exchange rate and interest rate derivatives.Forwards, futures, swap.Credit type derivatives are also covered.Other topics American and European style options,Pay Off
Report on Derivatives
Table of Contents
EXCHANGE RATE DERIVATIVES ...........................................................................3
1. Forward Contract ................................................................................................................. 3 Example ................................................................................................................................... 3 2. Currency Option................................................................................................................... 3 Example ................................................................................................................................... 4 3. Currency Futures.................................................................................................................. 4 Example ................................................................................................................................... 4
INTEREST RATE DERIVATIVES ..............................................................................5
4. Interest Rate Swaps .............................................................................................................. 5 Key Features: ........................................................................................................................... 5 Fixed and Floating payments ................................................................................................... 6 Example of Quote .................................................................................................................... 6 Example of Swap ..................................................................................................................... 6 Example on calculation of Interest rate payments in an IRS ................................................... 7 Variants to the Standard Swap................................................................................................. 8 5. Interest Rate Futures ............................................................................................................ 9 Example 1: January 2003 ........................................................................................................ 9 Example 2: January 1998 ........................................................................................................ 9 Borrowers Hedge – Hedging a Commercial Paper issue ........................................................ 9 6. Forward Rate Agreements ................................................................................................. 10 Payoff formula ....................................................................................................................... 10 Payoff at contract expiration.................................................................................................. 11 Notation ................................................................................................................................. 11 Example ................................................................................................................................. 11 7. Currency Swap ................................................................................................................... 12 Example ................................................................................................................................. 13
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CREDIT DERIVATIVES .............................................................................................14
8. Credit Default Swap........................................................................................................... 14 Example ................................................................................................................................. 15 Advantages of CDS ............................................................................................................... 15 9. Credit Liked Notes ............................................................................................................. 16 Repackaging .......................................................................................................................... 16 Credit Linked Notes............................................................................................................... 16 Mechanism of CLN ............................................................................................................... 16 Protection Buyer in CLN ....................................................................................................... 17 10. Collateralized Debt Obligations ......................................................................................... 18 Introduction ........................................................................................................................... 18 The CDO structure................................................................................................................. 18 Advantages of CDO............................................................................................................... 18
EXOTIC OPTIONS.......................................................................................................19
Option style ............................................................................................................................... 19 American and European options............................................................................................ 19 Difference in value of American and European options ....................................................... 20 Exotic options ............................................................................................................................ 21 Exotic options with Non Vanilla exercise rights ................................................................... 21 Exotic options with standard exercise styles ......................................................................... 22 Asian option : Why and how was it developed? ................................................................... 22 Types of averaging ................................................................................................................ 24 Conclusion................................................................................................................................. 24
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EXCHANGE RATE DERIVATIVES
1. Forward Contract
A ?forward contract‘ or simply a ?forward‘ is a non-standardized contract between two parties to buy or sell an asset at a specified future time at a price agreed today. It costs nothing to enter a forward contract. The party agreeing to buy the underlying asset in the future assumes a long position, and the party agreeing to sell the asset in the future assumes a short position. The price agreed upon is called the delivery price, which is equal to the forward price at the time the contract is entered into. Forwards Contracts can be used to hedge risk (typically currency or exchange rate risk), as a means of speculation, or to allow a party to take advantage of a quality of the underlying instrument which is time-sensitive. Pay- Off The value of a forward position at maturity depends on the relationship between the delivery price (K) and the underlying price (ST) at that time. For a long position this payoff is: fT = ST ? K For a short position, it is: fT = K ? ST Example Ram wants to buy a house a year from now and at the same time;Shyam wants to sell his Rs. 2 Lacs house one year from now. They both enter in a Forward Contract assuming the sale price in one year time of say 2.25L. Ram is in a long position, while Shyam enters into a short position. Now, after one year if the market valuation of the house is 2.5 L, Shyam will have made a profit of .25L and Ram a potential loss by the same amount.
2. Currency Option ?Currency Option‘ or ?Option Contract‘ is a contract in which the under underlying asset is a foreign currency. The option gives the holder the right but not the obligation to buy (for a call) or sell (for a put) a set amount of the currency at a certain exchange rate on or before the expiration date. 3
It is largely used when international corporations wish to hedge against the possibility of adverse movements in foreign exchange rates. Corporations primarily use FX options to hedge uncertain future cash flows in a foreign currency. The general rule is to hedge certain foreign currency cash flows with forwards, and uncertain foreign cash flows with option. Example Customer enters into an Option contract to sell Rs. 1,000,000 and buy $20,000 on December 31.Pre-agreed exchange rate is 50 Rupees per Dollar. If rate moves to Rs. 51/dollar, then the option will be exercised, allowing the owner to sell Rupee at 50 and immediately buy it back in the spot market at 51, making a profit (Rs. 20,000) in the process. If Rupee gets stronger (say at Rs. 49/dollar) then the owner will let the option to expire and forfeit the option premium.
3. Currency Futures
?Currency Futures‘ or ?FX Future‘ is a ‘futures contract‘ to exchange one currency for another at a specified date in the future at a price (exchange rate) that is fixed on the purchase date. It is an Exchange traded currency contract. Typically, one of the currencies is the US dollar. The price of a future is then in terms of US dollars per unit of other currency. Investors use these futures contracts to hedge against foreign exchange risk. Though, most contracts are closed out before that as it can be done at any time prior to the contract's delivery date. It is mandatory for both the parties to honor the contract. Currency futures can also be used to speculate and, by incurring a risk, attempt to profit from rising or falling exchange rate. Example Customer enters into a futures contract to sell Rs. 1,000,000 and buy $20,000 on December 31.Pre-agreed exchange rate is 50 Rupees per Dollar. If rate moves to Rs. 51/dollar at contract expiration, then the owner will sell Rupee at 50 and immediately buy it back in the spot market at 51, making a profit (Rs. 20,000) in the process. If rate moves to Rs. 49/dollar at contract expiration, then the owner will still have to sell Rupee at 50 and after buying back in the spot market at 49, the person will incur a loss (Rs. 20,000) in the process. 4
INTEREST RATE DERIVATIVES
Swaps
Financial Swaps are a funding technique which permit a borrower to access one market and then exchange the liability for another type of liability. Investors can exchange one type of asset for another with a preferred income stream. They are a device to obtain the desired form of financing indirectly which otherwise might be inaccessible or too expensive.
4. Interest Rate Swaps
A standard fixed-to-floating interest rate swap, also known as ?exchange of borrowings? or ?coupon swap? or in market jargon the Plain Vanilla swap is an agreement between two parties in which each contracts to make payments to the other on particular dates in the future till a specified termination date. One party, known as the fixed rate payer, makes fixed payments all of which are determined at the outset. The other party known as the floating rate payer will make payments which depend on the movements of a specified interest rate index (such as the 6 month LIBOR). Key Features: 1. Notional Principal The fixed and floating principal is calculated on a specific sum called as notional principal. The parties do not exchange this amount at any time. In a standard swap, the notional principal remains constant through the life of the swap. 2. The Fixed Rate The rate applied to the notional principal to calculate the size of the fixed payment. The banks who are market makers quote the fixed rate they are willing to pay if they are the fixed rate payers in the swap and the fixed rate payments they are willing to receive if they are the floating rate payer in the swap. 3. The Floating rate In a standard swap, the floating rate is generally a market index such as LIBOR, prime rate, T-Bill rate etc. The maturity of the underlying index equals the interval between the payment dates. 5
Fixed and Floating payments The fixed and floating payments are calculated as follows: Fixed Payment = P * Rfx * Ffx Floating Payment = P * Rfl * Ffl Where, P = Notional Principal, Rfx is fixed rate, Rfl is floating rate, Ffx is the fixed rate day count fraction and Ffl is the floating rate day count fraction. Example of Quote A bank might quote a US dollar floating to a fixed 5-yr swap rate as: Treasuries+30bp/Treasuries+50bp This quote means: 1. The bank is willing to make fixed rate payments at a rate that is 30 basis pts above the Treasury bill yield in return for receiving floating rate payments based on LIBOR. 2. The bank is willing to accept interest payments at a fixed rate of 50 basis points above the Treasury bill yield in return for paying floating rate payments based on LIBOR. Example of Swap
In the above example, party A is paying a floating rate and wants to pay fixed. Party B is paying fixed and wants to pay floating. After the swap, A pays fixed rate of 8.65 + (LIBOR+1.5) – (LIBOR+0.7) = 9.45%. Similarly Party B pays floating of LIBOR + 0.55%.
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In the above example, party A is paying a floating rate and wants to pay fixed. Party B is paying fixed and wants to pay floating. Bank acts as an intermediary. After the swap, A pays fixed rate of 8.65 + (LIBOR+1.5) – (LIBOR+0.55) = 9.60%. Similarly Party B pays floating of LIBOR + 0.7%. 30 basis points is the spread for the bank for carrying out the transaction. Example on calculation of Interest rate payments in an IRS A three year fixed-to-floating IRS: Notional Principal = $5 million Effective Date = September 1, 2010 Floating Rate = 6 month LIBOR. Fixed and floating rate dates Every March 1 and September 1 starting March 1 2011 till September 1 2013.Floating rate Reset Dates: 2 business days prior to the previous floating date payment. Fixed Payments:
Payment Date 1/3/1992 1/9/1992 1/3/1993 1/9/1993 1/3/1994 1/9/1994 Day count Fraction 182/360 184/360 181/360 184/360 181/360 184/360 Amount $2401388.9 $2427777.8 $2388194.4 $2427777.8 $2388194.4 $2427777.8
Trade Date: August 30, 2010 Fixed Rate: 9.5% p.a. payable semiannually.
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Suppose floating rates evolve as follows:
Reset Date 30/8/1991 28/2/1992 30/8/1992 27/8/1993 30/8/1993 27/8/1994 LIBOR (% p.a.) 9.80 9.20 9.50 8.90 9.70 10.20
Floating payments:
Payment Date 1/3/1992 1/9/1992 1/3/1993 1/9/1993 1/3/1994 1/9/1994 Amount($) 2477222.2 2351111.1 2388194.4 2274444.4 2438472.2 2606666.7
Normally, the payments are netted out with only the net payment being transferred from the deficit to the surplus party. Variants to the Standard Swap 1. Notional Principal may change instead of being constant. 2. The setting of floating rate may not be the value of the index on setting date but an average of the values of the index from a pre specified set of dates. 3. A basis swap involves an exchange of 2 floating payments, each tied to a different floating index. 4. A callable swap allows the fixed interest payer to terminate the swap before maturity and in a puttable swap the fixed payment receiver has this choice. 5. In a forward start swap, the effective date is months or even years ahead of the trade date.
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5. Interest Rate Futures
? Interest rate futures are used by Corporations, banks and Financial Institutions to hedge interest rate risk. ? While the name ?interest rate futures‘ suggests that the underlying is interest rate, it is actually bonds that form the underlying instruments ? Price of IRF is determined by demand and supply, which in turn are determined by the individual investor‘s views on interest rate movements in the future. ? Interest rates are inversely related to prices of bonds, which form the underlying of IRF.
Example 1: January 2003 ? On 1/1/2003, the notional 10-year bond (from ZCYC) was Rs.45.43. ? ? ? You believe the long rate will go up, so you short three futures contracts (12,000 bonds) @ Rs.49. On 31/1/2003, the notional 10-year bond is at Rs.39. You have a profit of Rs.10/bond or Rs.120, 000 overall.
Example 2: January 1998 ? On 9 January 1998, the notional 10-year bond was at Rs.32. ? ? ? ? ? The 31/1/1998 futures were trading at Rs.33. You thought interest rates would go down, so you purchased two futures contracts (8000 bonds) @ Rs.33. Interest rates went up! On expiration, the notional bond was at Rs.21.4. A loss of Rs.92, 800.
Borrowers Hedge – Hedging a Commercial Paper issue ? In January, A Corp. plans to issue $50 million 90-day Commercial Paper (CP) around May. ? Paper of comparable Quality yields 12.05%. At this yield the Corp. realizes 50mn – (12.05%*50mn*90/360) = $48,493,750. ? Corp. uses IRF to hedge against interest rate fluctuations. 9
? Consider June 90-day T-Bill trades at 89.75(Discount of 11.25%) ? In mid-January, Corp. plans to issue $50mn of 90-day CP in 4 months. Sells 50 T-Bill June contracts at 89.75. ? In mid-May, Yields have risen. Hence, Corp. must issue its paper at a yield of 12.5%. In this case it realizes $48,437,500 (calculated as previously). ? This is a shortfall of $56,250. ? June T-bill futures are trading at 89.45. Corp. buys 50 contracts for a profit of 30 ticks on each contract. Each tick is worth $25. Payoff from Futures = (30*25*50) = $37,500. ? The gain on futures partially covers for the shortfall on the CP issue.
6. Forward Rate Agreements
A forward rate agreement (FRA) is a forward contract in which one party pays a fixed interest rate, and receives a floating interest rate equal to a reference rate (the underlying rate). The payments are calculated over a notional amount over a certain period, and netted; i.e. only the differential is paid. It is paid on the effective date. The reference rate is fixed one or two days before the effective date, dependent on the market convention for the particular currency. FRAs are over-the counter derivatives. A swap is a combination of FRAs. Payoff formula The netted payment made at the effective date is as follows ?????????????? = ???????????????? ???????????? ? ? ? ? ?????????????????? ???????? ? ?????????? ???????? ? ?? 1 + ?????????????????? ???????? ? ??
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The Fixed Rate is the rate at which the contract is agreed. The Reference Rate is typically Euribor or LIBOR. ? is the day count fraction, i.e. the portion of a year over which the rates are calculated, using the day count convention used in the money markets in the underlying currency. For EUR and USD this is generally the number of days divided by 360. The Fixed Rate and Reference Rate are rates that should accrue over a period starting on the effective date, and then paid at the end of the period (termination date). However, as the payment is already known at the beginning of the period, it is also paid at the beginning. This is why the discount factor is used in the denominator.
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Payoff at contract expiration ? Floating rate > Contract rate: Long receives a payment ? Floating rate < Contract rate: Long makes a payment Notation A 2 x 3 FRA, contract expires in 2 months and the underlying loan is settled in 3 months, is shown as follows:
Example ? On March 1, 2010 Company XYZ finds out that it needs $10 million on June 1, 2010. ? Company can repay the amount on September 1, 2010 through the sales generated by it. Normal Circumstances • Company will borrow $10 m on June 1 @ LIBOR + 100 basis points Under FRA ? XYZ gets a 3x6 FRA quote from a dealer. Suppose dealer quotes 7% ? On June 1, the company will pay off the difference between 7% and LIBOR Benefit/Loss on June 1 ? Company loses if LIBOR < 7% ? Company gains if LIBOR > 7%
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7. Currency Swap
In a currency swap, one party makes payments denominated in one currency, while the payments from the other party are made in other currency. Typically, the notional amount of the contract, expressed in both currencies at the current exchange rate, are exchanged at contract initiation and returned at the contract termination in the same amounts. As an example of what motivates a currency swap, consider a U.S firm, Party A, wishes to establish operation in Australia and wants to finance the cost in Australian dollars (AUD). The firm finds, however, that issuing debt in AUD is relatively more expensive than issuing USDdenominated debt, because they are relatively unknown in Australian financial markets. An alternative to issuing AUD-denominated debt is to issue USD debt and enter into an USD.AUD currency swap. Through a swaps facilitator, the U.S firm finds an Australian firm, Party B, that faces the same situation in reverse. They wish to issue AUD debt and swap into a USD exposure. There are four possible types of currency swaps available: ? Party A pays fixed rate on AUD received, and Party B pays a fixed rate on USD received ? Party A pays floating rate on AUD received, and Party B pays a fixed rate on USD received ? Party A pays fixed rate on AUD received, and Party B pays a floating rate on USD received ? Party A pays floating rate on AUD received, and Party B pays a floating rate on USD received Steps for fixed-for-fixed currency swap: 1. Notional principal is swapped at initiation. Party A gives USD to Party B and gets AUD back. This is done because the motivation of Party A was to get AUD and the motivation of Party B was to get USD 2. Interest payments are made without netting because the payments are made in different currencies. Party A, who got USD, pays the U.S interest rate on the notional amount of USD received to Party A. 3. At the termination of the swap agreement (maturity), the counterparties give each other back the exchanged notional amounts. Notional principal is swapped again at the termination of the agreement.
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Example AA is an Australian citizen company and BB is an US citizen company. AA needs USD 1 million for doing business in U.S while BB requires AUD 2 million to do business in Australia. BB can borrow in US at 9% while AA can borrow in US at 10%. AA can borrow in Australia at 7% while BB will have to pay 8%. The Exchange rate is 2 AUD/USD. They decide to borrow locally and swap the borrowed funds, charging each other the rate the other party would have paid had they borrowed in the foreign market. The swap period of five years. Initial Borrowing from Domestic Banks ? AA borrows AUD 2 million @ 7%, annual interest payment: AUD 140,000 annually ? BB borrows USD 1 million @ 9%, annual interest payment: AUD 90,000 annually Swap Initiation ? AA gets USD 1 million, agreeing to pay BB 10% interest annually in USD ? BB gets AUD 2 million, agreeing to pay AA 8% interest annually in AUD Swap Interest Payments ? AA owes USD 100,000 while BB owes AUD 160,000 annually ? AA pays Australian bank AUD 140,000 (but receives AUD 160,000 annually from BB) ? BB pays US bank USD 90,000 (but receives USD 100,000 from AA)
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Swap Termination (returning the notional principal) ? AA gets back AUD 2 million from BB and pays back to the Australian bank ? BB gets back USD 1 million from AA and pays back to the US bank Benefits ? Gain of AUD 20,000 annually for AA ? Gain of USD 10,000 annually for BB ? Both gain the same considering the exchange rate of 2 AUD/USD
CREDIT DERIVATIVES
8. Credit Default Swap
A credit default swap (CDS) is a swap contract in which the protection buyer of the CDS makes a series of payments (often referred to as the CDS "fee" or "spread") to the protection seller and, in exchange, receives a payoff if a credit instrument (typically a bond or loan) experiences a credit event. In its simplest form, a credit default swap is a bilateral contract between the buyer and seller of protection. The CDS will refer to a ?reference entity" or "reference obligor", usually a corporation or government. The reference entity is not a party to the contract. The protection buyer makes quarterly premium payments—the ?spread?—to the protection seller. If the reference entity defaults, the protection seller pays the buyer the par value of the bond in exchange for physical delivery of the bond, although settlement may also be by cash or auction. A default is referred to as a ?credit event? and includes such events as failure to pay, restructuring and bankruptcy. A holder of a bond may ?buy protection? to hedge its risk of default. In this way, a CDS is similar to credit insurance, although CDS are not similar to or subject to regulations governing casualty or life insurance. Also, investors can buy and sell protection without owning any debt of the reference entity.
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Example ? XYZ enters into 2-year CDS on notional amount of USD 10 million on 10-year bonds issued by ABC corporation ? Annual premium to be paid is 55 basis points ? ABC defaults in first year and bonds trading at 60 cents to a dollar CDS working ? XYZ first year premium payment = .0055 * USD 10m = $55,000 to the seller of CDS ? XYZ will receive payment of $4,000,000 = (1 – 0.6) * USD 10 million from the seller of CDS if ABC defaults in bond payments Advantages of CDS ? Risk Management: Credit risk can be managed separate to interest rate risk ? Short Positions:Shorting the bond is costly and challenging, if it is in high demand in the market. By CDS you can gain a short position in the fixed income security. ? Liquidity:Credit derivative market is more liquid in US than the cash market. ? Flexibility Credit derivatives facilitate credit, maturity and currency positions not otherwise available in the underlying cash market. Also customized contract can be developed using 2 or more CDS. For example, if an investor wanted a position with a 4-year maturity, a customized contract could be devised using 3-year and 5-year maturity swaps. ? Confidentiality CDS are OTC contracts and confidential. In contrast, in a loan, the issuer has knowledge of the contract.
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9. Credit Liked Notes
Repackaging Repackaging involves placing securities in a Special Purpose Vehicle (SPV), which then issues customized notes that are backed by the instruments in the SPV. The goal is to take securities with attractive features that are nevertheless unappealing /inaccessible to many investors and repackage them to create viable investments that are not otherwise available to the investor. A security may be unappealing/ inaccessible because it is denominated in a foreign currency, does not trade locally, or because of onerous tax features. Credit Linked Notes A credit-linked note (CLN) is a special form of repackaging that is often directly issued by a corporate issuer. Credit-Linked Notes (CLN) is structured securities whose principal and interest payments are contingent on the performance of specified borrower companies, or Reference Entities. They are created by embedding a Credit Default Swap (CDS) in a funded asset to form an investment whose credit risk and cash flow characteristics resemble those of a bond or loan. Mechanism of CLN Typically the bank selects a reference entity and sells protection using a credit default swap, (CDS), on that selected reference entity. Selling protection would mean the bank received a regular fixed payment from the CDS counterparty. The bank then issues the CLN. The CLN would be for the same principal amount and maturity as the CDS. The final terms of the CLN would mirror the terms in the CDS transaction. The CLN investor would pay cash to the bank to buy the note. The bank would pay the investor regular interest until the maturity of the note.Provided there is no credit event by the reference entity the investor receives back the principal investment on the maturity of the note. In case a credit event occurs, the reference party incurs a credit loss i. The CDS on which the bank sold protection is triggered. The bank pays to the CDS counterparty the principal amount of the CDS in cash. The bank receives in return a deliverable instrument normally a bond that was issued by the reference entity that is now in default. ii. The CLN is also triggered. The investor does not get his principal returned, instead the bank on-delivers the bond to the CLN buyer.
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The investor will have experienced a loss as a result of the credit event because the delivered bond will be worth less than the original sum invested. The scale of the loss incurred will depend on the market value of the delivered bond. Protection Buyer in CLN Usually, the SPV puts the proceeds of the note issuance in collateral. If the reference entity defaults, the SPV liquidates the collateral and simply pays less principal back to the note investors. This ‘spared‘ amount is directly passed through to the protection buyer (a bank) in the DS. Since the SPV has a very high rating (usually AAA), the bank is not exposed to a significant counterparty default risk in the DS (it were exposed if it had contracted the DS with the investors directly). CLN Investor An investor (e.g. an investment management fund) may be prohibited from buying bonds rated below AAA. The SPV‘s rating is AAA, which refers to its ?ability to pay ‘, but not its ?obligation to pay‘. So the fund is allowed to invest into the CLN, although it is essentially investing into the riskier reference asset (it bears the losses associated with them). Thus a CLN can be used to circumvent certain investment constraints in order to enhance yields. The investor has the credit risk on the reference entity as well as the CLN issuer and therefore obtains a higher return on the CLN than would have been achieved on a normal medium term note. Furthermore, CLNs are also relatively simple to book from the buyer's perspective they are often regarded as cash instruments rather than derivatives. This means the investor does not need to enter into an ISDA master agreement. The final terms that accompany the CLN will contain the detailed information concerning the workings of the transaction. CLN Seller The issuer receives cash from the sale of the CLN. This has two advantages. First it can mean that the cost of funding for the issuer can be at or below the target cost of funding. Second because the issuer has cash it means that the embedded CDS is effectively 100% cash collateralized, (remember that the issuer is selling protection to the market place but buying protection from the investor). If there is a credit event the issuer is in control of the cash and is not dependent on the performance of the investor, (as it would normally be the case with a CDS).
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10. Collateralized Debt Obligations
Introduction A Collateralized Debt Obligation (CDO) is a credit derivative that creates fixed income securities with widely different risk characteristics from a pool of risky assets. The coupon and principal payments of these securities are linked to the performance of the underlying pool of assets like bank high yield bonds (CBO) or bank leverage loans (CLO). The CDO structure A CDO is a special purpose company or vehicle (SPV), complete with assets, liabilities and a manager.
The portfolio of assets is transferred to the SPV that funds these assets, from cash proceeds from the set of investors. The CDO structure allocates interest income and principal repayment from a pool of different debt instruments to a prioritized collection of securities notes called tranches. Senior notes (often rated AA or AAA) are paid before mezzanine and other lower rated notes. Any residual cash flow is paid to the equity piece. Defaults "flood the bottom," so to speak, at first and then rise up the totem pole. At the bottom, the equity tranche absorbs the first defaults. This makes the equity tranches the most risky but enjoys the highest yield. The senior CDO liabilities are significantly less risky than the collateral but receive only a constant amount of returns from the CDO. Hence the default risk of the portfolio of assets is transferred to the tranches across various levels, through the CDO. Advantages of CDO 1. Banks (who initially owns the portfolio of assets): a. Transfer risk: Transfer credit risk (default risk) to the investors. b. Monetize: The banks wants to liquidate the asset before the majority. c. Shrink the balance sheet: Bank sometimes wants to shrink its balance sheet to meet some needs like: accounting (avoid consolidation), rules and regulations (minimize capital required by Basel I/II) 18
2. Investors: a. Higher Yields: They receive relatively higher yields compared to the other available market traded securities. b. Caters to all segment of markets: There is a possibility of hedging, speculation and arbitrage which satisfies all the needs of an investor c. Leverage: High leverage position can be taken whereby investors invest in the CDO without actually owning the assets. 3. SPV: Earns a fee for just transferring the risk from one party to another.
EXOTIC OPTIONS
Option style
In finance, the style or family of an option is a general term denoting the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of options are either European or American (style) options. These options - as well as others where the payoff is calculated similarly - are referred to as "vanilla options". Options where the payoff is calculated differently are categorized as "exotic options". Exotic options can pose challenging problems in valuation and hedging. American and European options The key difference between American and European options relates to when the options can be exercised: ? A European option may be exercised only at the expiry date of the option, i.e. at a single predefined point in time. ? An American option on the other hand may be exercised at any time before the expiry date. For both, the pay-off - when it occurs - is via: Max [ (S – K), 0 ], for a call option Max [ (K – S), 0 ], for a put option: (Where K is the Strike price and S is the spot price of the underlying asset) Option contracts traded on futures exchanges are mainly American-style, whereas those traded over-the-counter are mainly European. Nearly all stock and equity options are American options, while indexes are generally represented by European options.
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Difference in value of American and European options European options are typically valued using the Black-Scholes or Black model formula. There are no general formulae for American options, but a choice of models to approximate the price is available (for example Whaley, binomial options model, and others - there is no consensus on which is preferable). An investor holding an American-style option and seeking optimal value will only exercise it before maturity under certain circumstances. Any option has a non-negative time value and is usually worth more unexercised. Owners who wish to realize the full value of their option will mostly prefer to sell it on, rather than exercise it immediately, sacrificing the time value. Where an American and a European option are otherwise identical (having the same strike price, etc.), the American option will be worth at least as much as the European (which it entails). If it is worth more, then the difference is a guide to the likelihood of early exercise. In practice, one can calculate the Black-Scholes price of a European option that is equivalent to the American option (except for the exercise dates of course). The difference between the two prices can then be used to calibrate the more complex American option model. To account for the American's higher value there must be some situations in which it is optimal to exercise the American option before the expiration date. This can arise in several ways, such as: ? ? An in the money (ITM) call option on a stock is often exercised just before the stock pays a dividend which would lower its value by more than the option's remaining time value A deep ITM currency option (FX option) where the strike currency has a lower interest rate than the currency to be received will often be exercised early because the time value sacrificed is less valuable than the expected depreciation of the received currency against the strike. An American bond option on the dirty price of a bond (such as some convertible bonds) may be exercised immediately if ITM and a coupon are due. A put option on gold will be exercised early when deep ITM, because gold tends to hold its value whereas the currency used as the strike is often expected to lose value through inflation if the holder waits until final maturity to exercise the option (they will almost certainly exercise a contract deep ITM, minimizing its time value).
? ?
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Exotic options
In finance, an exotic option is a derivative which has features making it more complex than commonly traded products (vanilla options). These products are usually traded over-thecounter (OTC), or are embedded in structured notes. Consider an equity index. A straight call or put, either American or European would be considered non-exotic (vanilla). An exotic product could have one or more of the following features: ? The payoff at maturity depends not just on the value of the underlying index at maturity, but at its value at several times during the contract's life (it could be an Asian option depending on some average) It could depend on more than one index. There could be callability and putability rights. It could involve foreign exchange rates in various ways, such as a quanto option.
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Even products traded actively in the market can have the characteristics of exotic options, such as convertible bonds, whose valuation can depend on the price and volatility of the underlying equity, the credit rating, the level and volatility of interest rates, and the correlations between these factors. Given below are few examples of exotic options and a detailed explanation of an exotic option known as the Asian option. Exotic options with Non Vanilla exercise rights There are other, more unusual exercise styles in which the pay-off value remains the same as a standard option (as in the classic American and European options above) but where early exercise occurs differently: ? A Bermudan option is an option where the buyer has the right to exercise at a set (always discretely spaced) number of times. This is intermediate between a European option—which allows exercise at a single time, namely expiry—and an American option, which allows exercise at any time (the name is a pun: Bermuda is between America and Europe). For example a typical Bermudan swaption might confer the opportunity to enter into an interest rate swap. The option holder might decide to enter into the swap at the first exercise date (and so enter into, say, a ten-year swap) or defer and have the opportunity to enter in six months‘ time (and so enter a nine-year and six-month swap). Most exotic interest rate options are of Bermudan style. ? A Canary option is an option whose exercise style lies somewhere between European options and Bermudan options. (The name refers to the relative geography of the Canary Islands.) Typically, the holder can exercise the option at quarterly dates, but not before a set time period (typically one year) has elapsed. The term was coined by Keith Kline, who at the time was an agency fixed income trader at the Bank of New York. 21
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A capped-style option is not an interest rate cap but a conventional option with a predefined profit cap written into the contract. A capped-style option is automatically exercised when the underlying security closes at a price making the option's mark to market match the specified amount. A compound option is an option on another option, and as such presents the holder with two separate exercise dates and decisions. If the first exercise date arrives and the 'inner' option's market price is below the agreed strike the first option will be exercised (European style), giving the holder a further option at final maturity. A shout option allows the holder effectively two exercise dates: during the life of the option they can (at any time) "shout" to the seller that they are locking-in the current price, and if this gives them a better deal than the pay-off at maturity they'll use the underlying price on the shout date rather than the price at maturity to calculate their final pay-off. A swing option gives the purchaser the right to exercise one and only one call or put on any one of a number of specified exercise dates (this latter aspect is Bermudan). Penalties are imposed on the buyer if the net volume purchased exceeds or falls below specified upper and lower limits. Allows the buyer to "swing" the price of the underlying asset. Primarily used in energy trading.
Exotic options with standard exercise styles These options can be exercised either European style or American style; they differ from the plain vanilla option only in the calculation of their pay-off value: ? A cross option (or composite option) is an option on some underlying in one currency with a strike denominated in another currency. For example a standard call option on IBM, which is denominated in dollars pays $MAX(S-K,0) (where S is the stock price at maturity and K is the strike). A composite stock option might pay JPY MAX(S/Q-K,0), where Q is the prevailing FX rate. The pricing of such options naturally needs to take into account FX volatility and the correlation between the exchange rate of the two currencies involved and the underlying stock price. A quanto option is a cross option in which the exchange rate is fixed at the outset of the trade, typically at 1. The payoff of an IBM quanto call option would then be JPY max(SK,0). An exchange option is the right to exchange one asset for another (such as a sugar future for a corporate bond). A Low Exercise Price Option (LEPO) is a European style call option with a low exercise price of $0.01
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Asian option : Why and how was it developed? Asian options are so called because they were introduced in Tokyo, Japan, in 1987, at a branch of an American bank. An Asian option (or average value option) is a special type of option contract. For Asian options the payoff is determined by the average underlying price over some 22
pre-set period of time. This is different to the case of the usual European option and American option, where the payoff of the option contract depends on the price of the underlying instrument at maturity; Asian options are thus one of the basic forms of exotic options. One advantage of Asian options is that these reduce the risk of market manipulation of the underlying instrument at maturity. Asian options were designed to prevent option traders from attempting to manipulate the price of the underlying security on the exercise date. Another advantage of Asian options involves the relative cost of Asian options compared to European or American options. Because of the averaging feature, Asian options reduce the volatility inherent in the option; therefore, Asian options are typically cheaper than European or American options. This can be an advantage for corporations that are subject to the FASB revised Statement No. 123, which requires that corporations expense employee stock options. Permutations of Asian option There are numerous permutations of Asian option, the most basic are listed below:
Where A denotes the average, and K the strike. The floating strike (or floating rate) Asian call option has the payout where k is a weighting, usually 1 so often omitted from descriptions.
The equivalent put option payoff is given by
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Types of averaging The Average A may be obtained in many ways, conventionally this means an arithmetic average. In the continuous case this is obtained by
For the case of discrete monitoring (with monitoring at the times average given by
) we have the
There also exists an Asian option with geometric average, in the continuous case this is given by
Conclusion
In the current securities markets there are plenty of products available to the investor for the purpose of hedging and speculation. Each product has its set of benefits and complexity. Based on the risk appetite of the investor one must carefully select the instruments. These instruments are can also be selected based on the underlying of derivatives i.e. interest rates, foreign exchange etc.
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doc_664694049.pdf
It explains the Exchange rate and interest rate derivatives.Forwards, futures, swap.Credit type derivatives are also covered.Other topics American and European style options,Pay Off
Report on Derivatives
Table of Contents
EXCHANGE RATE DERIVATIVES ...........................................................................3
1. Forward Contract ................................................................................................................. 3 Example ................................................................................................................................... 3 2. Currency Option................................................................................................................... 3 Example ................................................................................................................................... 4 3. Currency Futures.................................................................................................................. 4 Example ................................................................................................................................... 4
INTEREST RATE DERIVATIVES ..............................................................................5
4. Interest Rate Swaps .............................................................................................................. 5 Key Features: ........................................................................................................................... 5 Fixed and Floating payments ................................................................................................... 6 Example of Quote .................................................................................................................... 6 Example of Swap ..................................................................................................................... 6 Example on calculation of Interest rate payments in an IRS ................................................... 7 Variants to the Standard Swap................................................................................................. 8 5. Interest Rate Futures ............................................................................................................ 9 Example 1: January 2003 ........................................................................................................ 9 Example 2: January 1998 ........................................................................................................ 9 Borrowers Hedge – Hedging a Commercial Paper issue ........................................................ 9 6. Forward Rate Agreements ................................................................................................. 10 Payoff formula ....................................................................................................................... 10 Payoff at contract expiration.................................................................................................. 11 Notation ................................................................................................................................. 11 Example ................................................................................................................................. 11 7. Currency Swap ................................................................................................................... 12 Example ................................................................................................................................. 13
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CREDIT DERIVATIVES .............................................................................................14
8. Credit Default Swap........................................................................................................... 14 Example ................................................................................................................................. 15 Advantages of CDS ............................................................................................................... 15 9. Credit Liked Notes ............................................................................................................. 16 Repackaging .......................................................................................................................... 16 Credit Linked Notes............................................................................................................... 16 Mechanism of CLN ............................................................................................................... 16 Protection Buyer in CLN ....................................................................................................... 17 10. Collateralized Debt Obligations ......................................................................................... 18 Introduction ........................................................................................................................... 18 The CDO structure................................................................................................................. 18 Advantages of CDO............................................................................................................... 18
EXOTIC OPTIONS.......................................................................................................19
Option style ............................................................................................................................... 19 American and European options............................................................................................ 19 Difference in value of American and European options ....................................................... 20 Exotic options ............................................................................................................................ 21 Exotic options with Non Vanilla exercise rights ................................................................... 21 Exotic options with standard exercise styles ......................................................................... 22 Asian option : Why and how was it developed? ................................................................... 22 Types of averaging ................................................................................................................ 24 Conclusion................................................................................................................................. 24
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EXCHANGE RATE DERIVATIVES
1. Forward Contract
A ?forward contract‘ or simply a ?forward‘ is a non-standardized contract between two parties to buy or sell an asset at a specified future time at a price agreed today. It costs nothing to enter a forward contract. The party agreeing to buy the underlying asset in the future assumes a long position, and the party agreeing to sell the asset in the future assumes a short position. The price agreed upon is called the delivery price, which is equal to the forward price at the time the contract is entered into. Forwards Contracts can be used to hedge risk (typically currency or exchange rate risk), as a means of speculation, or to allow a party to take advantage of a quality of the underlying instrument which is time-sensitive. Pay- Off The value of a forward position at maturity depends on the relationship between the delivery price (K) and the underlying price (ST) at that time. For a long position this payoff is: fT = ST ? K For a short position, it is: fT = K ? ST Example Ram wants to buy a house a year from now and at the same time;Shyam wants to sell his Rs. 2 Lacs house one year from now. They both enter in a Forward Contract assuming the sale price in one year time of say 2.25L. Ram is in a long position, while Shyam enters into a short position. Now, after one year if the market valuation of the house is 2.5 L, Shyam will have made a profit of .25L and Ram a potential loss by the same amount.
2. Currency Option ?Currency Option‘ or ?Option Contract‘ is a contract in which the under underlying asset is a foreign currency. The option gives the holder the right but not the obligation to buy (for a call) or sell (for a put) a set amount of the currency at a certain exchange rate on or before the expiration date. 3
It is largely used when international corporations wish to hedge against the possibility of adverse movements in foreign exchange rates. Corporations primarily use FX options to hedge uncertain future cash flows in a foreign currency. The general rule is to hedge certain foreign currency cash flows with forwards, and uncertain foreign cash flows with option. Example Customer enters into an Option contract to sell Rs. 1,000,000 and buy $20,000 on December 31.Pre-agreed exchange rate is 50 Rupees per Dollar. If rate moves to Rs. 51/dollar, then the option will be exercised, allowing the owner to sell Rupee at 50 and immediately buy it back in the spot market at 51, making a profit (Rs. 20,000) in the process. If Rupee gets stronger (say at Rs. 49/dollar) then the owner will let the option to expire and forfeit the option premium.
3. Currency Futures
?Currency Futures‘ or ?FX Future‘ is a ‘futures contract‘ to exchange one currency for another at a specified date in the future at a price (exchange rate) that is fixed on the purchase date. It is an Exchange traded currency contract. Typically, one of the currencies is the US dollar. The price of a future is then in terms of US dollars per unit of other currency. Investors use these futures contracts to hedge against foreign exchange risk. Though, most contracts are closed out before that as it can be done at any time prior to the contract's delivery date. It is mandatory for both the parties to honor the contract. Currency futures can also be used to speculate and, by incurring a risk, attempt to profit from rising or falling exchange rate. Example Customer enters into a futures contract to sell Rs. 1,000,000 and buy $20,000 on December 31.Pre-agreed exchange rate is 50 Rupees per Dollar. If rate moves to Rs. 51/dollar at contract expiration, then the owner will sell Rupee at 50 and immediately buy it back in the spot market at 51, making a profit (Rs. 20,000) in the process. If rate moves to Rs. 49/dollar at contract expiration, then the owner will still have to sell Rupee at 50 and after buying back in the spot market at 49, the person will incur a loss (Rs. 20,000) in the process. 4
INTEREST RATE DERIVATIVES
Swaps
Financial Swaps are a funding technique which permit a borrower to access one market and then exchange the liability for another type of liability. Investors can exchange one type of asset for another with a preferred income stream. They are a device to obtain the desired form of financing indirectly which otherwise might be inaccessible or too expensive.
4. Interest Rate Swaps
A standard fixed-to-floating interest rate swap, also known as ?exchange of borrowings? or ?coupon swap? or in market jargon the Plain Vanilla swap is an agreement between two parties in which each contracts to make payments to the other on particular dates in the future till a specified termination date. One party, known as the fixed rate payer, makes fixed payments all of which are determined at the outset. The other party known as the floating rate payer will make payments which depend on the movements of a specified interest rate index (such as the 6 month LIBOR). Key Features: 1. Notional Principal The fixed and floating principal is calculated on a specific sum called as notional principal. The parties do not exchange this amount at any time. In a standard swap, the notional principal remains constant through the life of the swap. 2. The Fixed Rate The rate applied to the notional principal to calculate the size of the fixed payment. The banks who are market makers quote the fixed rate they are willing to pay if they are the fixed rate payers in the swap and the fixed rate payments they are willing to receive if they are the floating rate payer in the swap. 3. The Floating rate In a standard swap, the floating rate is generally a market index such as LIBOR, prime rate, T-Bill rate etc. The maturity of the underlying index equals the interval between the payment dates. 5
Fixed and Floating payments The fixed and floating payments are calculated as follows: Fixed Payment = P * Rfx * Ffx Floating Payment = P * Rfl * Ffl Where, P = Notional Principal, Rfx is fixed rate, Rfl is floating rate, Ffx is the fixed rate day count fraction and Ffl is the floating rate day count fraction. Example of Quote A bank might quote a US dollar floating to a fixed 5-yr swap rate as: Treasuries+30bp/Treasuries+50bp This quote means: 1. The bank is willing to make fixed rate payments at a rate that is 30 basis pts above the Treasury bill yield in return for receiving floating rate payments based on LIBOR. 2. The bank is willing to accept interest payments at a fixed rate of 50 basis points above the Treasury bill yield in return for paying floating rate payments based on LIBOR. Example of Swap
In the above example, party A is paying a floating rate and wants to pay fixed. Party B is paying fixed and wants to pay floating. After the swap, A pays fixed rate of 8.65 + (LIBOR+1.5) – (LIBOR+0.7) = 9.45%. Similarly Party B pays floating of LIBOR + 0.55%.
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In the above example, party A is paying a floating rate and wants to pay fixed. Party B is paying fixed and wants to pay floating. Bank acts as an intermediary. After the swap, A pays fixed rate of 8.65 + (LIBOR+1.5) – (LIBOR+0.55) = 9.60%. Similarly Party B pays floating of LIBOR + 0.7%. 30 basis points is the spread for the bank for carrying out the transaction. Example on calculation of Interest rate payments in an IRS A three year fixed-to-floating IRS: Notional Principal = $5 million Effective Date = September 1, 2010 Floating Rate = 6 month LIBOR. Fixed and floating rate dates Every March 1 and September 1 starting March 1 2011 till September 1 2013.Floating rate Reset Dates: 2 business days prior to the previous floating date payment. Fixed Payments:
Payment Date 1/3/1992 1/9/1992 1/3/1993 1/9/1993 1/3/1994 1/9/1994 Day count Fraction 182/360 184/360 181/360 184/360 181/360 184/360 Amount $2401388.9 $2427777.8 $2388194.4 $2427777.8 $2388194.4 $2427777.8
Trade Date: August 30, 2010 Fixed Rate: 9.5% p.a. payable semiannually.
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Suppose floating rates evolve as follows:
Reset Date 30/8/1991 28/2/1992 30/8/1992 27/8/1993 30/8/1993 27/8/1994 LIBOR (% p.a.) 9.80 9.20 9.50 8.90 9.70 10.20
Floating payments:
Payment Date 1/3/1992 1/9/1992 1/3/1993 1/9/1993 1/3/1994 1/9/1994 Amount($) 2477222.2 2351111.1 2388194.4 2274444.4 2438472.2 2606666.7
Normally, the payments are netted out with only the net payment being transferred from the deficit to the surplus party. Variants to the Standard Swap 1. Notional Principal may change instead of being constant. 2. The setting of floating rate may not be the value of the index on setting date but an average of the values of the index from a pre specified set of dates. 3. A basis swap involves an exchange of 2 floating payments, each tied to a different floating index. 4. A callable swap allows the fixed interest payer to terminate the swap before maturity and in a puttable swap the fixed payment receiver has this choice. 5. In a forward start swap, the effective date is months or even years ahead of the trade date.
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5. Interest Rate Futures
? Interest rate futures are used by Corporations, banks and Financial Institutions to hedge interest rate risk. ? While the name ?interest rate futures‘ suggests that the underlying is interest rate, it is actually bonds that form the underlying instruments ? Price of IRF is determined by demand and supply, which in turn are determined by the individual investor‘s views on interest rate movements in the future. ? Interest rates are inversely related to prices of bonds, which form the underlying of IRF.
Example 1: January 2003 ? On 1/1/2003, the notional 10-year bond (from ZCYC) was Rs.45.43. ? ? ? You believe the long rate will go up, so you short three futures contracts (12,000 bonds) @ Rs.49. On 31/1/2003, the notional 10-year bond is at Rs.39. You have a profit of Rs.10/bond or Rs.120, 000 overall.
Example 2: January 1998 ? On 9 January 1998, the notional 10-year bond was at Rs.32. ? ? ? ? ? The 31/1/1998 futures were trading at Rs.33. You thought interest rates would go down, so you purchased two futures contracts (8000 bonds) @ Rs.33. Interest rates went up! On expiration, the notional bond was at Rs.21.4. A loss of Rs.92, 800.
Borrowers Hedge – Hedging a Commercial Paper issue ? In January, A Corp. plans to issue $50 million 90-day Commercial Paper (CP) around May. ? Paper of comparable Quality yields 12.05%. At this yield the Corp. realizes 50mn – (12.05%*50mn*90/360) = $48,493,750. ? Corp. uses IRF to hedge against interest rate fluctuations. 9
? Consider June 90-day T-Bill trades at 89.75(Discount of 11.25%) ? In mid-January, Corp. plans to issue $50mn of 90-day CP in 4 months. Sells 50 T-Bill June contracts at 89.75. ? In mid-May, Yields have risen. Hence, Corp. must issue its paper at a yield of 12.5%. In this case it realizes $48,437,500 (calculated as previously). ? This is a shortfall of $56,250. ? June T-bill futures are trading at 89.45. Corp. buys 50 contracts for a profit of 30 ticks on each contract. Each tick is worth $25. Payoff from Futures = (30*25*50) = $37,500. ? The gain on futures partially covers for the shortfall on the CP issue.
6. Forward Rate Agreements
A forward rate agreement (FRA) is a forward contract in which one party pays a fixed interest rate, and receives a floating interest rate equal to a reference rate (the underlying rate). The payments are calculated over a notional amount over a certain period, and netted; i.e. only the differential is paid. It is paid on the effective date. The reference rate is fixed one or two days before the effective date, dependent on the market convention for the particular currency. FRAs are over-the counter derivatives. A swap is a combination of FRAs. Payoff formula The netted payment made at the effective date is as follows ?????????????? = ???????????????? ???????????? ? ? ? ? ?????????????????? ???????? ? ?????????? ???????? ? ?? 1 + ?????????????????? ???????? ? ??
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The Fixed Rate is the rate at which the contract is agreed. The Reference Rate is typically Euribor or LIBOR. ? is the day count fraction, i.e. the portion of a year over which the rates are calculated, using the day count convention used in the money markets in the underlying currency. For EUR and USD this is generally the number of days divided by 360. The Fixed Rate and Reference Rate are rates that should accrue over a period starting on the effective date, and then paid at the end of the period (termination date). However, as the payment is already known at the beginning of the period, it is also paid at the beginning. This is why the discount factor is used in the denominator.
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Payoff at contract expiration ? Floating rate > Contract rate: Long receives a payment ? Floating rate < Contract rate: Long makes a payment Notation A 2 x 3 FRA, contract expires in 2 months and the underlying loan is settled in 3 months, is shown as follows:
Example ? On March 1, 2010 Company XYZ finds out that it needs $10 million on June 1, 2010. ? Company can repay the amount on September 1, 2010 through the sales generated by it. Normal Circumstances • Company will borrow $10 m on June 1 @ LIBOR + 100 basis points Under FRA ? XYZ gets a 3x6 FRA quote from a dealer. Suppose dealer quotes 7% ? On June 1, the company will pay off the difference between 7% and LIBOR Benefit/Loss on June 1 ? Company loses if LIBOR < 7% ? Company gains if LIBOR > 7%
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7. Currency Swap
In a currency swap, one party makes payments denominated in one currency, while the payments from the other party are made in other currency. Typically, the notional amount of the contract, expressed in both currencies at the current exchange rate, are exchanged at contract initiation and returned at the contract termination in the same amounts. As an example of what motivates a currency swap, consider a U.S firm, Party A, wishes to establish operation in Australia and wants to finance the cost in Australian dollars (AUD). The firm finds, however, that issuing debt in AUD is relatively more expensive than issuing USDdenominated debt, because they are relatively unknown in Australian financial markets. An alternative to issuing AUD-denominated debt is to issue USD debt and enter into an USD.AUD currency swap. Through a swaps facilitator, the U.S firm finds an Australian firm, Party B, that faces the same situation in reverse. They wish to issue AUD debt and swap into a USD exposure. There are four possible types of currency swaps available: ? Party A pays fixed rate on AUD received, and Party B pays a fixed rate on USD received ? Party A pays floating rate on AUD received, and Party B pays a fixed rate on USD received ? Party A pays fixed rate on AUD received, and Party B pays a floating rate on USD received ? Party A pays floating rate on AUD received, and Party B pays a floating rate on USD received Steps for fixed-for-fixed currency swap: 1. Notional principal is swapped at initiation. Party A gives USD to Party B and gets AUD back. This is done because the motivation of Party A was to get AUD and the motivation of Party B was to get USD 2. Interest payments are made without netting because the payments are made in different currencies. Party A, who got USD, pays the U.S interest rate on the notional amount of USD received to Party A. 3. At the termination of the swap agreement (maturity), the counterparties give each other back the exchanged notional amounts. Notional principal is swapped again at the termination of the agreement.
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Example AA is an Australian citizen company and BB is an US citizen company. AA needs USD 1 million for doing business in U.S while BB requires AUD 2 million to do business in Australia. BB can borrow in US at 9% while AA can borrow in US at 10%. AA can borrow in Australia at 7% while BB will have to pay 8%. The Exchange rate is 2 AUD/USD. They decide to borrow locally and swap the borrowed funds, charging each other the rate the other party would have paid had they borrowed in the foreign market. The swap period of five years. Initial Borrowing from Domestic Banks ? AA borrows AUD 2 million @ 7%, annual interest payment: AUD 140,000 annually ? BB borrows USD 1 million @ 9%, annual interest payment: AUD 90,000 annually Swap Initiation ? AA gets USD 1 million, agreeing to pay BB 10% interest annually in USD ? BB gets AUD 2 million, agreeing to pay AA 8% interest annually in AUD Swap Interest Payments ? AA owes USD 100,000 while BB owes AUD 160,000 annually ? AA pays Australian bank AUD 140,000 (but receives AUD 160,000 annually from BB) ? BB pays US bank USD 90,000 (but receives USD 100,000 from AA)
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Swap Termination (returning the notional principal) ? AA gets back AUD 2 million from BB and pays back to the Australian bank ? BB gets back USD 1 million from AA and pays back to the US bank Benefits ? Gain of AUD 20,000 annually for AA ? Gain of USD 10,000 annually for BB ? Both gain the same considering the exchange rate of 2 AUD/USD
CREDIT DERIVATIVES
8. Credit Default Swap
A credit default swap (CDS) is a swap contract in which the protection buyer of the CDS makes a series of payments (often referred to as the CDS "fee" or "spread") to the protection seller and, in exchange, receives a payoff if a credit instrument (typically a bond or loan) experiences a credit event. In its simplest form, a credit default swap is a bilateral contract between the buyer and seller of protection. The CDS will refer to a ?reference entity" or "reference obligor", usually a corporation or government. The reference entity is not a party to the contract. The protection buyer makes quarterly premium payments—the ?spread?—to the protection seller. If the reference entity defaults, the protection seller pays the buyer the par value of the bond in exchange for physical delivery of the bond, although settlement may also be by cash or auction. A default is referred to as a ?credit event? and includes such events as failure to pay, restructuring and bankruptcy. A holder of a bond may ?buy protection? to hedge its risk of default. In this way, a CDS is similar to credit insurance, although CDS are not similar to or subject to regulations governing casualty or life insurance. Also, investors can buy and sell protection without owning any debt of the reference entity.
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Example ? XYZ enters into 2-year CDS on notional amount of USD 10 million on 10-year bonds issued by ABC corporation ? Annual premium to be paid is 55 basis points ? ABC defaults in first year and bonds trading at 60 cents to a dollar CDS working ? XYZ first year premium payment = .0055 * USD 10m = $55,000 to the seller of CDS ? XYZ will receive payment of $4,000,000 = (1 – 0.6) * USD 10 million from the seller of CDS if ABC defaults in bond payments Advantages of CDS ? Risk Management: Credit risk can be managed separate to interest rate risk ? Short Positions:Shorting the bond is costly and challenging, if it is in high demand in the market. By CDS you can gain a short position in the fixed income security. ? Liquidity:Credit derivative market is more liquid in US than the cash market. ? Flexibility Credit derivatives facilitate credit, maturity and currency positions not otherwise available in the underlying cash market. Also customized contract can be developed using 2 or more CDS. For example, if an investor wanted a position with a 4-year maturity, a customized contract could be devised using 3-year and 5-year maturity swaps. ? Confidentiality CDS are OTC contracts and confidential. In contrast, in a loan, the issuer has knowledge of the contract.
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9. Credit Liked Notes
Repackaging Repackaging involves placing securities in a Special Purpose Vehicle (SPV), which then issues customized notes that are backed by the instruments in the SPV. The goal is to take securities with attractive features that are nevertheless unappealing /inaccessible to many investors and repackage them to create viable investments that are not otherwise available to the investor. A security may be unappealing/ inaccessible because it is denominated in a foreign currency, does not trade locally, or because of onerous tax features. Credit Linked Notes A credit-linked note (CLN) is a special form of repackaging that is often directly issued by a corporate issuer. Credit-Linked Notes (CLN) is structured securities whose principal and interest payments are contingent on the performance of specified borrower companies, or Reference Entities. They are created by embedding a Credit Default Swap (CDS) in a funded asset to form an investment whose credit risk and cash flow characteristics resemble those of a bond or loan. Mechanism of CLN Typically the bank selects a reference entity and sells protection using a credit default swap, (CDS), on that selected reference entity. Selling protection would mean the bank received a regular fixed payment from the CDS counterparty. The bank then issues the CLN. The CLN would be for the same principal amount and maturity as the CDS. The final terms of the CLN would mirror the terms in the CDS transaction. The CLN investor would pay cash to the bank to buy the note. The bank would pay the investor regular interest until the maturity of the note.Provided there is no credit event by the reference entity the investor receives back the principal investment on the maturity of the note. In case a credit event occurs, the reference party incurs a credit loss i. The CDS on which the bank sold protection is triggered. The bank pays to the CDS counterparty the principal amount of the CDS in cash. The bank receives in return a deliverable instrument normally a bond that was issued by the reference entity that is now in default. ii. The CLN is also triggered. The investor does not get his principal returned, instead the bank on-delivers the bond to the CLN buyer.
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The investor will have experienced a loss as a result of the credit event because the delivered bond will be worth less than the original sum invested. The scale of the loss incurred will depend on the market value of the delivered bond. Protection Buyer in CLN Usually, the SPV puts the proceeds of the note issuance in collateral. If the reference entity defaults, the SPV liquidates the collateral and simply pays less principal back to the note investors. This ‘spared‘ amount is directly passed through to the protection buyer (a bank) in the DS. Since the SPV has a very high rating (usually AAA), the bank is not exposed to a significant counterparty default risk in the DS (it were exposed if it had contracted the DS with the investors directly). CLN Investor An investor (e.g. an investment management fund) may be prohibited from buying bonds rated below AAA. The SPV‘s rating is AAA, which refers to its ?ability to pay ‘, but not its ?obligation to pay‘. So the fund is allowed to invest into the CLN, although it is essentially investing into the riskier reference asset (it bears the losses associated with them). Thus a CLN can be used to circumvent certain investment constraints in order to enhance yields. The investor has the credit risk on the reference entity as well as the CLN issuer and therefore obtains a higher return on the CLN than would have been achieved on a normal medium term note. Furthermore, CLNs are also relatively simple to book from the buyer's perspective they are often regarded as cash instruments rather than derivatives. This means the investor does not need to enter into an ISDA master agreement. The final terms that accompany the CLN will contain the detailed information concerning the workings of the transaction. CLN Seller The issuer receives cash from the sale of the CLN. This has two advantages. First it can mean that the cost of funding for the issuer can be at or below the target cost of funding. Second because the issuer has cash it means that the embedded CDS is effectively 100% cash collateralized, (remember that the issuer is selling protection to the market place but buying protection from the investor). If there is a credit event the issuer is in control of the cash and is not dependent on the performance of the investor, (as it would normally be the case with a CDS).
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10. Collateralized Debt Obligations
Introduction A Collateralized Debt Obligation (CDO) is a credit derivative that creates fixed income securities with widely different risk characteristics from a pool of risky assets. The coupon and principal payments of these securities are linked to the performance of the underlying pool of assets like bank high yield bonds (CBO) or bank leverage loans (CLO). The CDO structure A CDO is a special purpose company or vehicle (SPV), complete with assets, liabilities and a manager.
The portfolio of assets is transferred to the SPV that funds these assets, from cash proceeds from the set of investors. The CDO structure allocates interest income and principal repayment from a pool of different debt instruments to a prioritized collection of securities notes called tranches. Senior notes (often rated AA or AAA) are paid before mezzanine and other lower rated notes. Any residual cash flow is paid to the equity piece. Defaults "flood the bottom," so to speak, at first and then rise up the totem pole. At the bottom, the equity tranche absorbs the first defaults. This makes the equity tranches the most risky but enjoys the highest yield. The senior CDO liabilities are significantly less risky than the collateral but receive only a constant amount of returns from the CDO. Hence the default risk of the portfolio of assets is transferred to the tranches across various levels, through the CDO. Advantages of CDO 1. Banks (who initially owns the portfolio of assets): a. Transfer risk: Transfer credit risk (default risk) to the investors. b. Monetize: The banks wants to liquidate the asset before the majority. c. Shrink the balance sheet: Bank sometimes wants to shrink its balance sheet to meet some needs like: accounting (avoid consolidation), rules and regulations (minimize capital required by Basel I/II) 18
2. Investors: a. Higher Yields: They receive relatively higher yields compared to the other available market traded securities. b. Caters to all segment of markets: There is a possibility of hedging, speculation and arbitrage which satisfies all the needs of an investor c. Leverage: High leverage position can be taken whereby investors invest in the CDO without actually owning the assets. 3. SPV: Earns a fee for just transferring the risk from one party to another.
EXOTIC OPTIONS
Option style
In finance, the style or family of an option is a general term denoting the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of options are either European or American (style) options. These options - as well as others where the payoff is calculated similarly - are referred to as "vanilla options". Options where the payoff is calculated differently are categorized as "exotic options". Exotic options can pose challenging problems in valuation and hedging. American and European options The key difference between American and European options relates to when the options can be exercised: ? A European option may be exercised only at the expiry date of the option, i.e. at a single predefined point in time. ? An American option on the other hand may be exercised at any time before the expiry date. For both, the pay-off - when it occurs - is via: Max [ (S – K), 0 ], for a call option Max [ (K – S), 0 ], for a put option: (Where K is the Strike price and S is the spot price of the underlying asset) Option contracts traded on futures exchanges are mainly American-style, whereas those traded over-the-counter are mainly European. Nearly all stock and equity options are American options, while indexes are generally represented by European options.
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Difference in value of American and European options European options are typically valued using the Black-Scholes or Black model formula. There are no general formulae for American options, but a choice of models to approximate the price is available (for example Whaley, binomial options model, and others - there is no consensus on which is preferable). An investor holding an American-style option and seeking optimal value will only exercise it before maturity under certain circumstances. Any option has a non-negative time value and is usually worth more unexercised. Owners who wish to realize the full value of their option will mostly prefer to sell it on, rather than exercise it immediately, sacrificing the time value. Where an American and a European option are otherwise identical (having the same strike price, etc.), the American option will be worth at least as much as the European (which it entails). If it is worth more, then the difference is a guide to the likelihood of early exercise. In practice, one can calculate the Black-Scholes price of a European option that is equivalent to the American option (except for the exercise dates of course). The difference between the two prices can then be used to calibrate the more complex American option model. To account for the American's higher value there must be some situations in which it is optimal to exercise the American option before the expiration date. This can arise in several ways, such as: ? ? An in the money (ITM) call option on a stock is often exercised just before the stock pays a dividend which would lower its value by more than the option's remaining time value A deep ITM currency option (FX option) where the strike currency has a lower interest rate than the currency to be received will often be exercised early because the time value sacrificed is less valuable than the expected depreciation of the received currency against the strike. An American bond option on the dirty price of a bond (such as some convertible bonds) may be exercised immediately if ITM and a coupon are due. A put option on gold will be exercised early when deep ITM, because gold tends to hold its value whereas the currency used as the strike is often expected to lose value through inflation if the holder waits until final maturity to exercise the option (they will almost certainly exercise a contract deep ITM, minimizing its time value).
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Exotic options
In finance, an exotic option is a derivative which has features making it more complex than commonly traded products (vanilla options). These products are usually traded over-thecounter (OTC), or are embedded in structured notes. Consider an equity index. A straight call or put, either American or European would be considered non-exotic (vanilla). An exotic product could have one or more of the following features: ? The payoff at maturity depends not just on the value of the underlying index at maturity, but at its value at several times during the contract's life (it could be an Asian option depending on some average) It could depend on more than one index. There could be callability and putability rights. It could involve foreign exchange rates in various ways, such as a quanto option.
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Even products traded actively in the market can have the characteristics of exotic options, such as convertible bonds, whose valuation can depend on the price and volatility of the underlying equity, the credit rating, the level and volatility of interest rates, and the correlations between these factors. Given below are few examples of exotic options and a detailed explanation of an exotic option known as the Asian option. Exotic options with Non Vanilla exercise rights There are other, more unusual exercise styles in which the pay-off value remains the same as a standard option (as in the classic American and European options above) but where early exercise occurs differently: ? A Bermudan option is an option where the buyer has the right to exercise at a set (always discretely spaced) number of times. This is intermediate between a European option—which allows exercise at a single time, namely expiry—and an American option, which allows exercise at any time (the name is a pun: Bermuda is between America and Europe). For example a typical Bermudan swaption might confer the opportunity to enter into an interest rate swap. The option holder might decide to enter into the swap at the first exercise date (and so enter into, say, a ten-year swap) or defer and have the opportunity to enter in six months‘ time (and so enter a nine-year and six-month swap). Most exotic interest rate options are of Bermudan style. ? A Canary option is an option whose exercise style lies somewhere between European options and Bermudan options. (The name refers to the relative geography of the Canary Islands.) Typically, the holder can exercise the option at quarterly dates, but not before a set time period (typically one year) has elapsed. The term was coined by Keith Kline, who at the time was an agency fixed income trader at the Bank of New York. 21
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A capped-style option is not an interest rate cap but a conventional option with a predefined profit cap written into the contract. A capped-style option is automatically exercised when the underlying security closes at a price making the option's mark to market match the specified amount. A compound option is an option on another option, and as such presents the holder with two separate exercise dates and decisions. If the first exercise date arrives and the 'inner' option's market price is below the agreed strike the first option will be exercised (European style), giving the holder a further option at final maturity. A shout option allows the holder effectively two exercise dates: during the life of the option they can (at any time) "shout" to the seller that they are locking-in the current price, and if this gives them a better deal than the pay-off at maturity they'll use the underlying price on the shout date rather than the price at maturity to calculate their final pay-off. A swing option gives the purchaser the right to exercise one and only one call or put on any one of a number of specified exercise dates (this latter aspect is Bermudan). Penalties are imposed on the buyer if the net volume purchased exceeds or falls below specified upper and lower limits. Allows the buyer to "swing" the price of the underlying asset. Primarily used in energy trading.
Exotic options with standard exercise styles These options can be exercised either European style or American style; they differ from the plain vanilla option only in the calculation of their pay-off value: ? A cross option (or composite option) is an option on some underlying in one currency with a strike denominated in another currency. For example a standard call option on IBM, which is denominated in dollars pays $MAX(S-K,0) (where S is the stock price at maturity and K is the strike). A composite stock option might pay JPY MAX(S/Q-K,0), where Q is the prevailing FX rate. The pricing of such options naturally needs to take into account FX volatility and the correlation between the exchange rate of the two currencies involved and the underlying stock price. A quanto option is a cross option in which the exchange rate is fixed at the outset of the trade, typically at 1. The payoff of an IBM quanto call option would then be JPY max(SK,0). An exchange option is the right to exchange one asset for another (such as a sugar future for a corporate bond). A Low Exercise Price Option (LEPO) is a European style call option with a low exercise price of $0.01
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Asian option : Why and how was it developed? Asian options are so called because they were introduced in Tokyo, Japan, in 1987, at a branch of an American bank. An Asian option (or average value option) is a special type of option contract. For Asian options the payoff is determined by the average underlying price over some 22
pre-set period of time. This is different to the case of the usual European option and American option, where the payoff of the option contract depends on the price of the underlying instrument at maturity; Asian options are thus one of the basic forms of exotic options. One advantage of Asian options is that these reduce the risk of market manipulation of the underlying instrument at maturity. Asian options were designed to prevent option traders from attempting to manipulate the price of the underlying security on the exercise date. Another advantage of Asian options involves the relative cost of Asian options compared to European or American options. Because of the averaging feature, Asian options reduce the volatility inherent in the option; therefore, Asian options are typically cheaper than European or American options. This can be an advantage for corporations that are subject to the FASB revised Statement No. 123, which requires that corporations expense employee stock options. Permutations of Asian option There are numerous permutations of Asian option, the most basic are listed below:
Where A denotes the average, and K the strike. The floating strike (or floating rate) Asian call option has the payout where k is a weighting, usually 1 so often omitted from descriptions.
The equivalent put option payoff is given by
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Types of averaging The Average A may be obtained in many ways, conventionally this means an arithmetic average. In the continuous case this is obtained by
For the case of discrete monitoring (with monitoring at the times average given by
) we have the
There also exists an Asian option with geometric average, in the continuous case this is given by
Conclusion
In the current securities markets there are plenty of products available to the investor for the purpose of hedging and speculation. Each product has its set of benefits and complexity. Based on the risk appetite of the investor one must carefully select the instruments. These instruments are can also be selected based on the underlying of derivatives i.e. interest rates, foreign exchange etc.
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