Description
Highlights the hedging foreign currency exposure using options with the help of detailed example.
Hedging Foreign Currency Exposure using options
? A contract giving the purchaser the right to
buy or sell a given amount of foreign exchange at a fixed price per unit for a specified time period ? Standard contract size is $1m in the bank market ? Available on major currencies like Pound, DM, Sfr, Yen, and C$ against USD ? Are also available on exchanges like Philadelphia Stock Exchange, LIFFE
? A variety of contracts on 8 currencies and 2
cross rate pairs with American and European style pricing ? Customized options are also availableexercise price, expiration date up to 2 years, premium quotation form (units of currency or percentage of underlying value) are chosen by the customer ? Dollar denominated delivery currency options with European style exercise on the DM, Yen are available; cash settled in USD
Option quotations and prices
? TN-1 ? Consider the Aug 58.5 Call option ? Spot Rate: $0.5851 is the spot dollar price of
one DM ? Strike Price: $0.5850/DM ? Premium: 0.50 cents per mark or $0.0050/DM; no trading of Sep and Dec on that day ? Total cost of 1 contract = DM 62500 * $0.0050/DM = $312.50
Foreign Currency Specualtion
Current quotes for DM: Spot Rate = $0.5851/DM 6 month forward rate = $0.5760/DM Expected spot rate after 6 months = $0.6 A) Speculate in the spot market 1) Use $100,000 and buy DM 170,910.96 2) Hold DM indefinitely (the trader is not committed to 6 months horizon) 3) Sell DM at the expected spot rate (if it materializes); receive $102,546.57 4) Profit = $2546.57
? ? ? ?
B) Speculating in the forward market: ? Today buy DM 173611.11 forward six months at the forward quote of 0.5760 (this step requires no cash outlay) ? In six months, receive DM for a cost of $100,000 ? Simultaneously sell DM in the spot market and receive $104,166.67 ? Profit = $4166.67
Speculating in options market
? Buyer of a call (e.g. buy a call option on DM at a
strike price of $0.5850 and a premium of $$0.005/DM); would not exercise at spot rates below 59 cents ? Writer of call- the opposite is true ? Buyer of put- exercise below 58 cents ? Writer of put- opposite
Option Pricing and Valuation
? ? ? ? ? ? ? ?
Garman-Kohlhagen Model (1983) Based on 6 factors: Spot rate Time to maturity Forward rate for matching maturity US dollar interest rate Foreign currency interest rate Volatility, standard deviation of daily spot price movement, annualized
? FX options are priced around the forward rate
? The formula calculates a subjective probability
distribution centered on the forward rate
? C= S (e-rf t ) N(d1) – X (e-rd t ) N(d2)
? P = X (e-rd t ) N(-d2) - S (e-rf t ) N(-d1)
? d1 = [ln(S/X) + (rd –rf +Var/2)T]/SD (Sqrt T) ? d2= d1 - SD (Sqrt T)
FX option greeks
? Delta– Spot rate sensitivity
? Theta- Sensitivity to time to maturity
? Lambda- Sensitivity to volatility ? Rho and phi- sensitivity to domestic and foreign
interest rates
Hedging Transactions Exposure
? Transaction Exposure: measures changes in the
value of outstanding financial obligations incurred prior to a change in exchange rates but not due to be settled until after the exchange rate change ? Operating Exposure: measures change in the PV of the firm resulting from any change in the future operating cash flows of the firm caused by an unexpected change in exchange rates ? Translation exposure: potential for accounting derived changes in owners’ equity to occur because of the need to translate foreign currency financial statements of foreign affiliates into a single reporting currency to prepare consolidated financial statements
Hedging transaction exposures
? A UK firm has concluded the sale of turbine to a US firm for 1m
? ? ? ? ? ? ? ? ? ?
?
pounds Sale is made in March and payment is due in June Market information: Spot exchange rate: $1.7640/pound 3 month forward rate: 1.7540 (a 2.2676% p.a. discount on the pound) Firm’s cost of capital: 12% UK 3 month borrowing interest rate: 10% UK 3 month investment rate: 8% US 3 month borrowing interest rate: 8% US 3 month investment interest rate: 6% June put option in the OTC market for 1m: strike $1.75, 1.5% premium Expected spot rate in 3 months: $1.76
Alternatives
? Remain unhedged
? Hedge in the forward market
? Hedge in the money market ? Hedge in the options market
Unhedged Position
? Expected receipts = 1m pounds * $1.76 =
1,76,000 ? If the pound falls to 1.65, receives 1.65m
Forward Market Hedge
? Sell 1m pound forward at 1.7540
? Less than unhedged position because the
forecast is different from the forward rate
Money market hedge
? Borrow in one currency and exchange the ? ?
? ?
proceeds for another currency Repay the loan from the business operations Borrow pounds, immediately convert the borrowed pounds into dollars and repay the loan from the sale proceeds Amount to be borrowed= 1m/1.025 = 975,610 Convert into dollars at the spot rate of 1.7640 receiving $1,720,976 today
Money market vs. Forward hedge
? Loan proceeds are received today, forward
proceeds are received after 3 months ? Calculate either the FV of loan or PV of forward ? Lets find FV ? Can invest dollar in money market instruments @ say, 6%, make a dollar loan @ 8%, invest the loan in the general operations of the firm @ 12% cost of capital
? Money market hedge is superior if loan proceeds
are invested at 7.7% or more
Options market hedge
? Can cover the exposure by purchasing a put option ? Can purchase either an ATM option at a strike price of
? ? ? ?
$1.75 (premium of 1.5%) or an OTM option at a strike of 1.71 (premium of 1%) Cost of option = size of option * premium * spot rate First option: 1m * 0.015 * 1.7640 = $26,460 Project the option cost by three months @12% = $27,254 When the 1m is received in June, the value in USD depends on the spot rate then
? Upside is unlimited ? At any rate above 1.75, firm would allow its option ? ? ? ?
expire If the expected rate of 1.76 materializes, firm would exchange 1m pound for $1.76m Net Proceeds = 1.76m – 27,254 = $1,742,746 Pound must appreciate enough above the 1.7540 forward rate to cover the cost of the option Break even upside spot price must be 1.7540 + 0.0273 = 1.7813
Comparison of alternatives
? TN-2
? Actual choice depends on risk tolerance and view
of the CFO
doc_556316740.pptx
Highlights the hedging foreign currency exposure using options with the help of detailed example.
Hedging Foreign Currency Exposure using options
? A contract giving the purchaser the right to
buy or sell a given amount of foreign exchange at a fixed price per unit for a specified time period ? Standard contract size is $1m in the bank market ? Available on major currencies like Pound, DM, Sfr, Yen, and C$ against USD ? Are also available on exchanges like Philadelphia Stock Exchange, LIFFE
? A variety of contracts on 8 currencies and 2
cross rate pairs with American and European style pricing ? Customized options are also availableexercise price, expiration date up to 2 years, premium quotation form (units of currency or percentage of underlying value) are chosen by the customer ? Dollar denominated delivery currency options with European style exercise on the DM, Yen are available; cash settled in USD
Option quotations and prices
? TN-1 ? Consider the Aug 58.5 Call option ? Spot Rate: $0.5851 is the spot dollar price of
one DM ? Strike Price: $0.5850/DM ? Premium: 0.50 cents per mark or $0.0050/DM; no trading of Sep and Dec on that day ? Total cost of 1 contract = DM 62500 * $0.0050/DM = $312.50
Foreign Currency Specualtion
Current quotes for DM: Spot Rate = $0.5851/DM 6 month forward rate = $0.5760/DM Expected spot rate after 6 months = $0.6 A) Speculate in the spot market 1) Use $100,000 and buy DM 170,910.96 2) Hold DM indefinitely (the trader is not committed to 6 months horizon) 3) Sell DM at the expected spot rate (if it materializes); receive $102,546.57 4) Profit = $2546.57
? ? ? ?
B) Speculating in the forward market: ? Today buy DM 173611.11 forward six months at the forward quote of 0.5760 (this step requires no cash outlay) ? In six months, receive DM for a cost of $100,000 ? Simultaneously sell DM in the spot market and receive $104,166.67 ? Profit = $4166.67
Speculating in options market
? Buyer of a call (e.g. buy a call option on DM at a
strike price of $0.5850 and a premium of $$0.005/DM); would not exercise at spot rates below 59 cents ? Writer of call- the opposite is true ? Buyer of put- exercise below 58 cents ? Writer of put- opposite
Option Pricing and Valuation
? ? ? ? ? ? ? ?
Garman-Kohlhagen Model (1983) Based on 6 factors: Spot rate Time to maturity Forward rate for matching maturity US dollar interest rate Foreign currency interest rate Volatility, standard deviation of daily spot price movement, annualized
? FX options are priced around the forward rate
? The formula calculates a subjective probability
distribution centered on the forward rate
? C= S (e-rf t ) N(d1) – X (e-rd t ) N(d2)
? P = X (e-rd t ) N(-d2) - S (e-rf t ) N(-d1)
? d1 = [ln(S/X) + (rd –rf +Var/2)T]/SD (Sqrt T) ? d2= d1 - SD (Sqrt T)
FX option greeks
? Delta– Spot rate sensitivity
? Theta- Sensitivity to time to maturity
? Lambda- Sensitivity to volatility ? Rho and phi- sensitivity to domestic and foreign
interest rates
Hedging Transactions Exposure
? Transaction Exposure: measures changes in the
value of outstanding financial obligations incurred prior to a change in exchange rates but not due to be settled until after the exchange rate change ? Operating Exposure: measures change in the PV of the firm resulting from any change in the future operating cash flows of the firm caused by an unexpected change in exchange rates ? Translation exposure: potential for accounting derived changes in owners’ equity to occur because of the need to translate foreign currency financial statements of foreign affiliates into a single reporting currency to prepare consolidated financial statements
Hedging transaction exposures
? A UK firm has concluded the sale of turbine to a US firm for 1m
? ? ? ? ? ? ? ? ? ?
?
pounds Sale is made in March and payment is due in June Market information: Spot exchange rate: $1.7640/pound 3 month forward rate: 1.7540 (a 2.2676% p.a. discount on the pound) Firm’s cost of capital: 12% UK 3 month borrowing interest rate: 10% UK 3 month investment rate: 8% US 3 month borrowing interest rate: 8% US 3 month investment interest rate: 6% June put option in the OTC market for 1m: strike $1.75, 1.5% premium Expected spot rate in 3 months: $1.76
Alternatives
? Remain unhedged
? Hedge in the forward market
? Hedge in the money market ? Hedge in the options market
Unhedged Position
? Expected receipts = 1m pounds * $1.76 =
1,76,000 ? If the pound falls to 1.65, receives 1.65m
Forward Market Hedge
? Sell 1m pound forward at 1.7540
? Less than unhedged position because the
forecast is different from the forward rate
Money market hedge
? Borrow in one currency and exchange the ? ?
? ?
proceeds for another currency Repay the loan from the business operations Borrow pounds, immediately convert the borrowed pounds into dollars and repay the loan from the sale proceeds Amount to be borrowed= 1m/1.025 = 975,610 Convert into dollars at the spot rate of 1.7640 receiving $1,720,976 today
Money market vs. Forward hedge
? Loan proceeds are received today, forward
proceeds are received after 3 months ? Calculate either the FV of loan or PV of forward ? Lets find FV ? Can invest dollar in money market instruments @ say, 6%, make a dollar loan @ 8%, invest the loan in the general operations of the firm @ 12% cost of capital
? Money market hedge is superior if loan proceeds
are invested at 7.7% or more
Options market hedge
? Can cover the exposure by purchasing a put option ? Can purchase either an ATM option at a strike price of
? ? ? ?
$1.75 (premium of 1.5%) or an OTM option at a strike of 1.71 (premium of 1%) Cost of option = size of option * premium * spot rate First option: 1m * 0.015 * 1.7640 = $26,460 Project the option cost by three months @12% = $27,254 When the 1m is received in June, the value in USD depends on the spot rate then
? Upside is unlimited ? At any rate above 1.75, firm would allow its option ? ? ? ?
expire If the expected rate of 1.76 materializes, firm would exchange 1m pound for $1.76m Net Proceeds = 1.76m – 27,254 = $1,742,746 Pound must appreciate enough above the 1.7540 forward rate to cover the cost of the option Break even upside spot price must be 1.7540 + 0.0273 = 1.7813
Comparison of alternatives
? TN-2
? Actual choice depends on risk tolerance and view
of the CFO
doc_556316740.pptx