Introduction to Stochastic Calculus Applied to Finance

Maintaining the lucid style of its popular predecessor, this concise and accessible introduction covers the probabilistic techniques required to understand the most widely used financial models. Along with additional exercises, this edition presents fully updated material on stochastic volatility models and option pricing.

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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 Edition

Complements on discrete models, including Rogers' approach to the fundamental theorem of asset pricing and super-replication in incomplete markets



Discussions on local volatility, Dupire's formula, the change of numéraire techniques, forward measures, and the forward Libor model



A new chapter on credit risk modeling



An extension of the chapter on simulation with numerical experiments that illustrate variance reduction techniques and hedging strategies



Additional exercises and problems

Providing 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.