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 SciLab. Key topics covered include martingales, arbitrage, option pricing, and the Black-Scholes model.

chapter |5 pages


chapter Chapter 1|21 pages

Discrete-time models

chapter Chapter 2|13 pages

Optimal stopping problem and American options

chapter Chapter 3|35 pages

Brownian motion and stochastic differential equations

chapter Chapter 4|36 pages

The Black-Scholes model

chapter Chapter 5|25 pages

Option pricing and partial differential equations

chapter Chapter 6|24 pages

Interest rate models

chapter Chapter 7|21 pages

Asset models with jumps

chapter Chapter 8|12 pages

Credit risk models

chapter Chapter 9|28 pages

Simulation and algorithms for financial models