Derivative securities and difference methods.
This book is devoted to pricing financial derivatives with a partial differential equation approach. It has two parts, each with four chapters. Part I, entitled ``Partial Differential Equation in Finance'', is about problem formulations and closed-form solutions, if such solutions exist. Part II, entitled ``Numerical Methods for Derivative Securities'', is about numerical solutions by finite-difference methods; it also discusses the determination of the coefficients in the partial differential equations. The book covers a variety of topics in finance, such as forward and futures contracts, the Black-Scholes model, European and American type options, free boundary problems, barrier options, Asian options, lookback options, multi-asset options, interest rate models, interest rate derivatives, swaps, swaptions, caps, floors, and collars. The treatment is mathematically rigorous. There are exercises at the end of each chapter. For the chapters in Part II, computer projects are also given.
scientific article; zbMATH DE number 2108367