Damien Lamberton & Bernard Lapeyre 
Introduction to Stochastic Calculus Applied to Finance [PDF ebook] 

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, 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 as well as a new chapter on credit risk modeling. It contains many numerical experiments and real-world examples taken from the authors” own experiences. The book also provides all of the necessary stochastic calculus theory and implements some of the algorithms using Sci Lab. Key topics covered include martingales, arbitrage, option pricing, and the Black-Scholes model.