European Option Pricing Models: The Precursors Of The Black–Scholes–Merton Theory And Holes During Market Turbulence

The following sections are included:Chapter OutlineIntroductionPrecursors to the Black–Scholes ModelBachelier formulaSprenkle formulaBoness formulaSamuelson formulaHow the Black–Scholes Option Formula is ObtainedThe short storyThe differential equationThe derivation of the formulaPublication of the formulaTesting the formulaFinancial Theory and the Black–Scholes–Merton TheoryThe Black–Scholes–Merton theoryAnalytical formulasThe Black–Scholes ModelThe Black–Scholes model and CAPMAn alternative derivation of the Black–Scholes modelThe put-call parity relationshipExamplesThe Black Model for Commodity ContractsThe model for forward, futures, and option contractsThe put-call relationshipApplication of the CAPM Model to Forward and Futures ContractsAn application of the model to forward and futures contractsAn application to the derivation of the commodity option valuationAn application to commodity options and commodity futures optionsThe Holes in the Black–Scholes–Merton Theory and the Financial CrisisVolatility changesInterest rate changesBorrowing penaltiesShort-selling penaltiesTransaction costsTaxesDividendsTakeoversSummaryQuestionsAppendix A. The Cumulative Normal Distribution FunctionAppendix B. The Bivariate Normal Density FunctionReferences