Introduction to Stochastic Calculus Applied to Finance
Since the publication of the first edition of this book the area of mathematical finance has grown rapidly with financial analysts using more sophisticated mathematical concepts such as stochastic integration to describe the behavior of markets and to derive computing methods. Maintaining the lucid style of its popular predecessor Introduction to Stochastic Calculus Applied to Finance Second Edition incorporates some of these new techniques and concepts to provide an accessible up-to-date initiation to the field. New to the Second EditionComplements on discrete models including Rogers' approach to the fundamental theorem of asset pricing and super-replication in incomplete marketsDiscussions on local volatility Dupire's formula the change of numéraire techniques forward measures and the forward Libor model A new chapter on credit risk modelingAn extension of the chapter on simulation with numerical experiments that illustrate variance reduction techniques and hedging strategiesAdditional exercises and problemsProviding all of the necessary stochastic calculus theory the authors cover many key finance topics including martingales arbitrage option pricing American and European options the Black-Scholes model optimal hedging and the computer simulation of financial models. They succeed in producing a solid introduction to stochastic approaches used in the financial world.
