No-Arbitrage Pricing: Analytical and Numerical Methods demonstrates the importance of an analytical viewpoint for the theoretical analysis of pricing and hedging of options and other contingent claims. The authors illustrate that the majority of processes used in finance and mathematical finance are sufficiently regular; therefore, many efficient analytical tools are applicable. They also provide guidance for the development of efficient numerical methods and show how to apply these tools to several situations that are important in financial engineering and mathematical finance. Topics covered include the Black--Scholes equation and the eigenfunction expansion method.

Table of Contents

The Generalization of the Black--Scholes Equation. Contingent Claims of the European Type. The Wiener--Hopf Factorization and Perpetual American Options. Barrier Options. American Options: Finite Time Horizon. Bermudan Options. Asian Options. Locally Risk-Minimizing Hedging. American Options in Regime-Switching Models. Models with Stochastic Interest Rates and Stochastic Volatility Models. Affine and Quadratic Term Structure Models. The Eigenfunction Expansion Method in Multi-Factor Quadratic Term Structure Models.

Author Biography

University of Texas, Austin, Texas, USA