Stochastic Calculus for Finance

This book introduces key results essential for financial practitioners by means of concrete examples and a fully rigorous exposition.

This brief but full introduction to basic stochastic processes contains key results that have become essential for finance practitioners and provides a solid grounding for understanding the Black–Scholes option pricing model. Students, practitioners and researchers will benefit from the authors' rigorous, but unfussy, approach to technical issues.This book focuses specifically on the key results in stochastic processes that have become essential for finance practitioners to understand. The authors study the Wiener process and Itô integrals in some detail, with a focus on results needed for the Black–Scholes option pricing model. After developing the required martingale properties of this process, the construction of the integral and the Itô formula (proved in detail) become the centrepiece, both for theory and applications, and to provide concrete examples of stochastic differential equations used in finance. Finally, proofs of the existence, uniqueness and the Markov property of solutions of (general) stochastic equations complete the book. Using careful exposition and detailed proofs, this book is a far more accessible introduction to Itô calculus than most texts. Students, practitioners and researchers will benefit from its rigorous, but unfussy, approach to technical issues. Solutions to the exercises are available online.