1、Chapter 25 Exotic Options,Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012,1,Types of Exotics,Package Nonstandard American options Gap options Forward start options Cliquet options Compound options Chooser options Barrier options,Binary options Lookback options Shout

2、 options Asian options Options to exchange one asset for another Options involving several assets Volatility and Variance swaps,Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012,2,Packages (page 574),Portfolios of standard options Examples from Chapter 11: bull spread

3、s, bear spreads, straddles, etc Often structured to have zero cost One popular package is a range forward contract (see Chapter 16),Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012,3,Non-Standard American Options (page 575),Exercisable only on specific dates (Bermuda

4、ns) Early exercise allowed during only part of life (initial “l(fā)ock out” period) Strike price changes over the life (warrants, convertibles),Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012,4,Gap Options,Gap call pays ST K1 when ST K2 Gap put pays off K1 ST when ST K2

5、 Can be valued with a small modification to BSM,Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012,5,Forward Start Options (page 576),Option starts at a future time, T1 Implicit in employee stock option plans Often structured so that strike price equals asset price at

6、time T1 Value is then times the value of similar option starting today,Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012,6,Cliquet Option,A series of call or put options with rules determining how the strike price is determined For example, a cliquet might consist of

7、20 at-the-money three-month options. The total life would then be five years When one option expires a new similar at-the-money is comes into existence,Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012,7,Compound Option (page 577),Option to buy or sell an option Call

8、on call Put on call Call on put Put on put Can be valued analytically Price is quite low compared with a regular option,Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012,8,Chooser Option “As You Like It” (page 578),Option starts at time 0, matures at T2 At T1 (0 K, ot

9、herwise pays nothing. Value = S0e-qT N(d1),Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012,14,Decomposition of a Call Option,Long: Asset-or-Nothing option Short: Cash-or-Nothing option where payoff is K Value = S0e-qT N(d1) erT KN(d2),Options, Futures, and Other Der

10、ivatives, 8th Edition, Copyright John C. Hull 2012,15,Lookback Options (page 582-84),Floating lookback call pays ST Smin at time T (Allows buyer to buy stock at lowest observed price in some interval of time) Floating lookback put pays Smax ST at time T (Allows buyer to sell stock at highest observe

11、d price in some interval of time) Fixed lookback call pays max(SmaxK, 0) Fixed lookback put pays max(K Smin, 0) Analytic valuation for all types,Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012,16,Shout Options (page 584),Buyer can shout once during option life Final

12、 payoff is either Usual option payoff, max(ST K, 0), or Intrinsic value at time of shout, St K Payoff: max(ST St , 0) + St K Similar to lookback option but cheaper,Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012,17,Asian Options (page 584),Payoff related to average

13、stock price Average Price options pay: Call: max(Save K, 0) Put: max(K Save , 0) Average Strike options pay: Call: max(ST Save , 0) Put: max(Save ST , 0),Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012,18,Asian Options,No exact analytic valuation Can be approximatel

14、y valued by assuming that the average stock price is lognormally distributed,Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012,19,Exchange Options (page 586-87),Option to exchange one asset for another For example, an option to exchange one unit of U for one unit of V

15、 Payoff is max(VT UT, 0),Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012,20,Basket Options (page 587),A basket option is an option to buy or sell a portfolio of assets This can be valued by calculating the first two moments of the value of the basket at option matur

16、ity and then assuming it is lognormal,Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012,21,Volatility and Variance Swaps,Volatility swap is agreement to exchange the realized volatility between time 0 and time T for a prespecified fixed volatility with both being mult

17、iplied by a prespecified principal Variance swap is agreement to exchange the realized variance rate between time 0 and time T for a prespecified fixed variance rate with both being multiplied by a prespecified principal Daily return is assumed to be zero in calculating the volatility or variance ra

18、te,Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012,22,Variance Swap,The (risk-neutral) expected variance rate between times 0 and T can be calculated from the prices of European call and put options with different strikes and maturity T For any value of S*,Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012,23,Volatility Swap,Options, Futures, an