Description
This is a presentation describes exotic options and its classification.
Group-III, Finance
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Call/Put options -Plain Vanilla Products -well defined properties -traded actively on exchanges Exotic Options: -non standard products -OTC -designed by financial engineers
Hedging ? Tax/Accounting/Legal usefulness ? Designed to reflect future view Also, ? I-banks design to attract business
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Packages
Path-dependant Path-independent/Free range
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American Option with nonstandard features
Sample Features: ? Early Exercise-On Certain dates (Bermudan option) ? Early Exercise-During part of life of option ? Change in strike price during life ? All of the three
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Options that will start in future - not at time zero Example: Executive Option
Valuation at time zero e-rT1?[c *S1/S0]
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Options on options
Call
Call Put
Put
Call-on-call Call-on-put
Put-on-call Put-on-put
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a call-on-a-call giving the owner the right to buy in 1 month's time a 6 month 1.55 US dollar The strike price on the compound is the premium that we would pay in 1 month's time if we exercised the compound for the option expiring 6 months from that point in time. It could be a put-on-a-call giving the owner the right to sell in 1 month's time a 6 month 1.55 US dollar call
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‘as you like it’ option After a specified period- choice: put or call Value of ‘chooser option’ at T1
max(c,p)=max(c, c+Ke-r(T2-T1)-S1e-q(T2-T1))
for European option
=c+e-q(T2-T1)max(0,Ke-(r-q)(T2-T1)-S1)
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Discontinous pay-off profile Payoff to gap call ST-G if ST>K
0 otherwise Value of G must be greater than or less than K
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Value of Gap call option Cgap =[SN(d1)-Ke-rtN(d2)]+(K-G)e-rtN(d2) Payoff to gap put G-ST if K>ST 0 otherwise Value of Gap put option Pgap =[Ke-rtN(-d2)-SN(d1)]+(G-K)e-rtN(-d2)
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Protect the holder against a disastrous move in the underlying asset Premium of LC paid if expiry in the money Payoff of Pay later call option ST-K-LC if ST>K 0 otherwise [Cpaylater]t=[SN(d1)-Ke-rTN(d2)]t-[LCe-rTN(d2)]t [Ppaylater]t=[Ke-rTN(-d2)-SN(-d1)]t-[Lpe-rTN(-d2)]t
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Payoff is dependent on - certain time period ? certain price level Types -Knock-(out/in) option -Down-and-(out/in) call -Up-and-(out/in) call
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c=S0e-qTN(d1)-Ke-rTN(d2) p=Ke-rTN(-d2)-S0e-qTN(d1)
Options with discontinuous payoff ? Example: ? Cash-or-nothing call --payoff=0; if S0<K --payoff=Q; if S0>K value= Q*e-rT*N(d2) ? Asset-or-nothing call -- payoff=0; if S0<K --payoff=S0; if S0>K value= S0*e-rT*N(d1)
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Payoff : maximum/minimum asset price reached during life of option Payoff from European lookback call =Final asset price – minimum price
Payoff from European lookback put = Maximum price – Final asset price
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Holder can ‘shout ’ to the writer at one time during its life Payoff= max( usual payoff, intrinsic value at the time of shout)
Payoff = max(0,S(T)-S(t))+(S(t)-K)
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Payoff depends on average price of underlying asset ? Payoffs average price call max(0,Savg-K) average price put max(0,K-Savg) average strike call max(0,Savg-ST) average strike put max(0,ST-Savg) ? Can be valued by assuming (as an approximation) that the average stock price is lognormally distributed
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Exchange one currency asset for the other Exchange shares in one stock for shares in another stock For example, an option to exchange one unit of U for one unit of V Payoff is max(VT – UT, 0) Value of the option V0e-qvTN(d1)-U0e-quTN(d2)
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Rainbow Options Two or more risky assets in the option
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Basket Options Payoff depends on value of the portfolio of assets This can be valued by calculating the first two moments of the value of the basket and then assuming it is lognormal
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Involves approximately replicating an exotic option with a portfolio of vanilla options Underlying principle: if we match the value of an exotic option on some boundary , we have matched it at all interior points of the boundary
doc_428060340.pptx
This is a presentation describes exotic options and its classification.
Group-III, Finance
?
?
Call/Put options -Plain Vanilla Products -well defined properties -traded actively on exchanges Exotic Options: -non standard products -OTC -designed by financial engineers
Hedging ? Tax/Accounting/Legal usefulness ? Designed to reflect future view Also, ? I-banks design to attract business
?
?
Packages
Path-dependant Path-independent/Free range
?
?
?
American Option with nonstandard features
Sample Features: ? Early Exercise-On Certain dates (Bermudan option) ? Early Exercise-During part of life of option ? Change in strike price during life ? All of the three
?
?
Options that will start in future - not at time zero Example: Executive Option
Valuation at time zero e-rT1?[c *S1/S0]
?
?
Options on options
Call
Call Put
Put
Call-on-call Call-on-put
Put-on-call Put-on-put
?
?
?
a call-on-a-call giving the owner the right to buy in 1 month's time a 6 month 1.55 US dollar The strike price on the compound is the premium that we would pay in 1 month's time if we exercised the compound for the option expiring 6 months from that point in time. It could be a put-on-a-call giving the owner the right to sell in 1 month's time a 6 month 1.55 US dollar call
?
?
?
‘as you like it’ option After a specified period- choice: put or call Value of ‘chooser option’ at T1
max(c,p)=max(c, c+Ke-r(T2-T1)-S1e-q(T2-T1))
for European option
=c+e-q(T2-T1)max(0,Ke-(r-q)(T2-T1)-S1)
? ?
Discontinous pay-off profile Payoff to gap call ST-G if ST>K
0 otherwise Value of G must be greater than or less than K
?
Value of Gap call option Cgap =[SN(d1)-Ke-rtN(d2)]+(K-G)e-rtN(d2) Payoff to gap put G-ST if K>ST 0 otherwise Value of Gap put option Pgap =[Ke-rtN(-d2)-SN(d1)]+(G-K)e-rtN(-d2)
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?
?
? ?
? ?
Protect the holder against a disastrous move in the underlying asset Premium of LC paid if expiry in the money Payoff of Pay later call option ST-K-LC if ST>K 0 otherwise [Cpaylater]t=[SN(d1)-Ke-rTN(d2)]t-[LCe-rTN(d2)]t [Ppaylater]t=[Ke-rTN(-d2)-SN(-d1)]t-[Lpe-rTN(-d2)]t
?
?
Payoff is dependent on - certain time period ? certain price level Types -Knock-(out/in) option -Down-and-(out/in) call -Up-and-(out/in) call
?
?
c=S0e-qTN(d1)-Ke-rTN(d2) p=Ke-rTN(-d2)-S0e-qTN(d1)
Options with discontinuous payoff ? Example: ? Cash-or-nothing call --payoff=0; if S0<K --payoff=Q; if S0>K value= Q*e-rT*N(d2) ? Asset-or-nothing call -- payoff=0; if S0<K --payoff=S0; if S0>K value= S0*e-rT*N(d1)
?
?
Payoff : maximum/minimum asset price reached during life of option Payoff from European lookback call =Final asset price – minimum price
Payoff from European lookback put = Maximum price – Final asset price
?
?
?
Holder can ‘shout ’ to the writer at one time during its life Payoff= max( usual payoff, intrinsic value at the time of shout)
Payoff = max(0,S(T)-S(t))+(S(t)-K)
?
?
Payoff depends on average price of underlying asset ? Payoffs average price call max(0,Savg-K) average price put max(0,K-Savg) average strike call max(0,Savg-ST) average strike put max(0,ST-Savg) ? Can be valued by assuming (as an approximation) that the average stock price is lognormally distributed
?
? ?
?
?
?
Exchange one currency asset for the other Exchange shares in one stock for shares in another stock For example, an option to exchange one unit of U for one unit of V Payoff is max(VT – UT, 0) Value of the option V0e-qvTN(d1)-U0e-quTN(d2)
?
Rainbow Options Two or more risky assets in the option
?
Basket Options Payoff depends on value of the portfolio of assets This can be valued by calculating the first two moments of the value of the basket and then assuming it is lognormal
?
?
Involves approximately replicating an exotic option with a portfolio of vanilla options Underlying principle: if we match the value of an exotic option on some boundary , we have matched it at all interior points of the boundary
doc_428060340.pptx