This second edition - completely up to date with new exercises - provides a comprehensive and self-contained treatment of the probabilistic theory behind the risk-neutral valuation principle and its application to the pricing and hedging of financial derivatives. On the probabilistic side, both discrete- and continuous-time stochastic processes are treated, with special emphasis on martingale theory, stochastic integration and change-of-measure techniques. Based on firm probabilistic foundations, general properties of discrete- and continuous-time financial market models are discussed.
A mathematically precise and one-volume definitive reference for risk neutral valuation, and stochastic models, as well as hedging. Equivalent to an advanced Financial Mathematics degree course at Courant's? Only if they use this book as a textbook. Quite amazing in rigor for this field. Reviewed by a practitioner in risk and pricing models in industry, albeit not a stochastic quant by persuasion.
This is a well-written, self-contained introduction to asset pricing via equivalent martingale measures. Readers new to the subject will appreciate the introductory chapters that provide suitable coverage of rigorous probability theory, Lesbesgue integration, and measure theory. The value of this particular book seems to be comprehensiveness -- it provides much more material than a book like Baxter and Rennie's "Financial Calculus", however it does not motivate the use of equivalent martingale machinery as well as these authors. Thus, I'd use this book as a base to your studies of asset pricing, but go elsewhere if you're having trouble with the intuition behind the mathematics.