IF400 – Financial Derivatives Erwin Hammer, H19-V20 Notatark skrevet for emnet IF400 – Finansielle instrumenter. Notatarket her er omfattende og dekker anslagsvis 95% av pensumet. Kapittel 1 til 6 er gjennomgått i større detalj med flere utledninger enn det som er gitt i forelesninger og i læreboken. Fra kapittel 7 og utover har jeg heller forsøkt å komprimere stoffet til det aller viktigste. Ellers følger notasjonen i stor grad læreboken «Derivatives Markets» av McDonald. Contents IF400 – Financial Derivatives ............................................................................................................. 1 Chapter 1: Fixed Income ..................................................................................................................... 4 Bonds .................................................................................................................................................. 4 Forward Rates ................................................................................................................................... 5 Duration and Immunization ............................................................................................................. 7 Convexity ......................................................................................................................................... 10 Chapter 2: Forwards and Futures .................................................................................................... 11 Forwards .......................................................................................................................................... 11 Forward Pricing on Financial Assets ........................................................................................... 12 Forward Pricing on Currencies ..................................................................................................... 14 Forward Pricing on Commodities ................................................................................................. 15 The Lease Rate for Commodity Short Sales .............................................................................. 16 Pricing Commodity Forwards with Storage Costs ..................................................................... 17 Convenience Yields ........................................................................................................................ 17 Backwardation and Contango ....................................................................................................... 19 Forward Rate Agreements ............................................................................................................ 19 Valuing FRAs................................................................................................................................... 19 Futures ............................................................................................................................................. 21 Chapter 3: Swaps ............................................................................................................................... 21 Commodity Swaps .......................................................................................................................... 21 Interest Rate Swaps ....................................................................................................................... 23 Chapter 4: Options ............................................................................................................................. 25 Price Bounds on Calls .................................................................................................................... 26 Price Bounds on Puts..................................................................................................................... 28 Insurance Values on Options ........................................................................................................ 29 Call Options and Strikes ................................................................................................................ 30 1 Put Options and Strikes ................................................................................................................. 30 Call Prices and Time ...................................................................................................................... 31 Put Prices and Time ....................................................................................................................... 32 Decomposing Option Prices ......................................................................................................... 32 Early Exercise Optimality ............................................................................................................... 33 The Put-Call Parity ......................................................................................................................... 35 Put-Call Parity with Dividend Yields ............................................................................................. 38 Generalized Parity .......................................................................................................................... 38 Option Profits ................................................................................................................................... 39 Directional Option Strategies ........................................................................................................ 40 Volatility Strategies ......................................................................................................................... 42 Chapter 5: Binomial Option Pricing .................................................................................................. 44 Pricing by Replication..................................................................................................................... 44 Pricing Multi-Period European Options ....................................................................................... 46 Pricing American Options .............................................................................................................. 46 Options on Other Assets ............................................................................................................... 47 Chapter 6: The Black-Scholes Model .............................................................................................. 47 Assumptions .................................................................................................................................... 48 Pricing Options using Black-Scholes ........................................................................................... 48 Black-Scholes Pricing on Currency Assets ................................................................................ 49 Deriving the Option Greeks: A preliminary result ...................................................................... 50 Option Greeks: Delta ...................................................................................................................... 52 Option Greeks: Gamma ................................................................................................................. 54 Option Greeks: Theta ..................................................................................................................... 54 Option Greeks: Vega ...................................................................................................................... 56 Option Greeks: Rho ........................................................................................................................ 57 Implied Volatility .............................................................................................................................. 58 Market-Making and Delta Hedging .............................................................................................. 59 Gamma Hedging ............................................................................................................................. 61 Chapter 8: Exotic Options ................................................................................................................. 62 Currency Options ............................................................................................................................ 62 Asian Options .................................................................................................................................. 62 Barrier Options ................................................................................................................................ 63 Compound Options......................................................................................................................... 64 Gap Options .................................................................................................................................... 65 European Exchange Options ........................................................................................................ 66 2 Perpetual American Options ......................................................................................................... 67 Chapter 9: Basic Probability Theory ............................................................................................... 69 The Normal Distribution ................................................................................................................