This book presents techniques for valuing derivative securities at a level suitable for practitioners, students in doctoral programs in economics and finance, and those in masters-level programs in financial mathematics and computational finance. It provides the necessary mathematical tools from analysis, probability theory, the theory of stochastic processes, and stochastic calculus, making extensive use of examples. It also covers pricing theory, with emphasis on martingale methods. The chapters are organized around the assumptions made about the dynamics of underlying price processes. Readers begin with simple, discrete-time models that require little mathematical sophistication, proceed to the basic Black–Scholes theory, and then advance to continuous-time models with multiple risk sources. The second edition takes account of the major developments in the field since 2000. New topics include the use of simulation to price American-style derivatives, a new one-step approach to pricing options by inverting characteristic functions, and models that allow jumps in volatility and Markov-driven changes in regime. The new chapter on interest-rate derivatives includes extensive coverage of the LIBOR market model and an introduction to the modeling of credit risk. As a supplement to the text, the book contains an accompanying CD-ROM with user-friendly FORTRAN, C++, and VBA program components.

Contents:

• Introduction and Overview
• Mathematical Preparation
• Tools for Continuous-Time Models
• Dynamics-Free Pricing
• Pricing Under Bernoulli Dynamics
• Black–Scholes Dynamics
• American Options and “Exotics”
• Models with Uncertain Volatility
• Discontinuous Processes
• Interest-Rate Dynamics
• Simulation
• Solving P.D.E.s Numerically
• Programs

“An excellent state-of-the-art presentation that brings the reader up to speed in short and solid order. The reader will welcome the exposition of essential mathematical prerequisites that are succintly covered, along with a precise treatment of recent advances in modeling asset price processes with the richer probabilistic structure of discontinuous processes, in both its theoretical and operational aspects.”

“This second edition represents a refreshingly complete account of current developments in the burgeoning field of derivative securities. My call is that you should exercise your right to buy to finish in the money.”