by T W Epps (University of Virginia, USA)

The development of successful techniques for valuing derivative assets is among the most influential achievements of economic science. Pricing Derivative Securities presents the theory of financial derivatives in a way that emphasizes both its mathematical foundations and its practical implementation. The book's organization reveals its three distinctive features. Part I surveys the necessary tools of analysis, probability theory, and stochastic calculus, thus making the book self-contained. The chapters in Part II, Pricing Theory, are organized around the dynamics of the price processes of underlying assets, progressing from simple models to those that require considerable mathematical sophistication. The last part of the book is devoted to the empirical implementation of the pricing formulas developed in Part II, offering a detailed survey of numerical methods and providing a collection of programs in FORTRAN and C++.

• Preliminaries:
  • Introduction and Overview
  • Mathematical Preparation
  • Tools for Continuous-Time Models
• Pricing Theory:
  • Dynamics-Free Pricing
  • Pricing Under Bernoulli Dynamics
  • Black-Scholes Dynamics
  • American Options and ‘Exotics’
  • Models with Uncertain Volatility
  • Discontinuous Processes
  • Interest-Rate Dynamics
• Computational Methods:
  • Simulation
  • Solving PDEs Numerically
  • Programs