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.
