1. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.1 Exotic Options and Other Nonstandard Products Chapter 20

2. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.2 Types of Exotic Options Packages Nonstandard American options Forward start options Compound options Chooser options Barrier options Binary options

3. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.3 Types of Exotic Options continued Lookback options Shout options Asian options Options to exchange one asset for another Options involving several assets

4. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.4 Packages (page 432) Portfolios of standard options Examples from Chapter 10: bull spreads, bear spreads, straddles, etc Often structured to have zero cost One popular package is a range forward contract (See Figure 20.1)

5. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.5 Nonstandard American Options (page 432) Exercisable only on specific dates (Bermudans) Early exercise allowed during only part of life (e.g. there may be an initial “lock out” period) Strike price changes over the life

6. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.6 Forward Start Options (page 433) Option starts at a future time, T Most common in employee stock option plans Often structured so that strike price equals asset price at time T

7. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.7 Compound Option (page 433) Option to buy / sell an option Call on call Put on call Call on put Put on put Very sensitive to volatility

8. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.8 Chooser Option “As You Like It” (page 433) Option starts at time 0, matures at T 2 At T 1 (0 < T 1 < T 2 ) buyer chooses whether it is a put or call A few lines of algebra shows that this is a package

9. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.9 Chooser Option as a Package

10. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.10 Barrier Options (page 434) In options: come into existence only if asset price hits barrier before option maturity Out options: die if asset price hits barrier before option maturity

11. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.11 Barrier Options (continued) Up options: asset price must hit barrier from below Down options: asset price must hit barrier from above Option may be a put or a call Eight possible combinations

12. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.12 Parity Relations c = c ui + c uo c = c di + c do p = p ui + p uo p = p di + p do

13. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.13 Binary Options (page 434) Cash-or-nothing: pays Q if S > K at time T, otherwise pays 0. Value = e –rT Q N(d 2 ) Asset-or-nothing: pays S if S > K at time T, otherwise pays 0. Value = S 0 N(d 1 )

14. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.14 Decomposition of a Call Option Long Asset-or-Nothing option Short Cash-or-Nothing option where payoff is K Value = S 0 N(d 1 ) – e –rT KN(d 2 )

15. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.15 Lookback Options (page 435) Lookback call pays S T – S min at time T Allows buyer to buy stock at lowest observed price in some interval of time Lookback put pays S max – S T at time T Allows buyer to sell stock at highest observed price in some interval of time

16. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.16 Shout Options (page 435) Buyer can ‘shout’ once during option life Final payoff is either Usual option payoff, max(S T – K, 0), or Intrinsic value at time of shout, S  – K Payoff: max(S T – S , 0) + S  – K Similar to lookback option but cheaper How can a binomial tree be used to value a shout option?

17. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.17 Asian Options (page 436) Payoff related to average stock price Average Price options pay: max(S ave – K, 0) (call), or max(K – S ave, 0) (put) Average Strike options pay: max(S T – S ave, 0) (call), or max(S ave – S T, 0) (put)

18. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.18 Exchange Options (page 436) Option to exchange one asset for another When asset with price U can be exchanged for asset with price V payoff is max(V T – U T, 0) min(U T, V T ) =V T – max(V T – U T, 0) max(U T, V T ) =U T + max(V T – U T, 0)

19. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.19 Types of Mortgage-Backed Securities (MBSs) Pass-Through Collateralized Mortgage Obligation (CMO) Interest Only (IO) Principal Only (PO)

20. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.20 Variations on Vanilla Interest Rate Swaps (page 438) Principal different on two sides Payment frequency different on two sides Can be floating for floating instead of floating for fixed

21. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.21 Compounding Swaps (page 439) Interest is compounded instead of being paid In Business Snapshot 20.2 the fixed side is 6% compounded forward at 6.3% while the floating side is LIBOR plus 20 bps compounded forward at LIBOR plus 10 bps.

22. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.22 Currency Swaps (page 440) Fixed for fixed Fixed for floating Floating for floating

23. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.23 More Complex Swaps LIBOR-in-arrears swaps CMS and CMT swaps Differential swaps These swaps cannot be correctly valued by assuming that forward rates are realized. We must assume that the realized rate is the forward rate plus a “convexity adjustment”

24. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.24 Equity Swaps Total return on an equity index is exchanged periodically for a fixed or floating return See Business Snapshot 20.3 on page 442

25. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.25 Swaps with Embedded Options Accrual swaps Cancelable swaps Cancelable compounding swaps

26. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 20.26 Other Swaps Indexed principal swap Commodity swap Volatility swap Bizzarre deals: for example the P&G 5/30 swap ( See Business Snapshot 20.4)