The Heath–Jarrow–Morton Libor Model

The following sections are included:IntroductionWhy Caplets?A History of Caplet PricingBlack’s ModelThe Heath–Jarrow–Morton ModelThe HJM Libor ModelEXTENSION 25.1: Black’s Model for Pricing Commodity Options and CapletsThe AssumptionsPricing CapletsCaplet and Floorlet Pricing (CFP) DataCaplet Pricing ModelThe InputsObservable InputsThe Average Forward Rate VolatilityUnderstanding the HJM Libor ModelForward Rates and MartingalesRisk-Neutral ValuationActual versus Pseudo-probabilitiesCaps and FloorsCapsFloorletsCaplet–Floorlet ParityFloorsUsing the HJM Libor ModelThe GreeksDelta HedgingGamma HedgingAmerican Options, Futures, Swaptions, and Other DerivativesSummaryAppendixCasesQuestions and Problems