Numerical Methods in Finance

by L. C. G. Rogers, D. Talay

Overview

Numerical methods in finance has recently emerged as a new discipline at the intersection of probability theory, finance and numerical analysis. This book describes a wide variety of numerical methods used in financial analysis: computation of option prices, especially American option prices, by finite difference and other methods; numerical solution of portfolio management strategies; statistical procedures, identification of models; Monte Carlo methods; and numerical implications of stochastic volatilities. Lucid and concise, it covers both mathematical matters and practical issues in numerical problems. This book is an ideal resource for economists, probabilists and applied mathematicians working in finance.

Product Details

ISBN-13:	9780521061698
Publisher:	Cambridge University Press
Publication date:	04/24/2008
Series:	Publications of the Newton Institute , #13
Pages:	340
Product dimensions:	6.00(w) x 8.90(h) x 1.10(d)

Table of Contents

Introduction; 1. Convergence of numerical schemes for degenerate parabolic equations arising in finance theory G. Barles; 2. Continuous-time Monte Carlo methods and variance reduction Nigel J. Newton; 3. Recent advances in numerical methods for pricing derivative securities M. Broad and J. Detemple; 4. American options: a comparison of numerical methods F. AitSahlia and P. Carr; 5. Fast, accurate and inelegant valuation of American options Adriaan Joubert and L. C. G. Rogers; 6. Valuation of American options in a jump-diffusion model Xiao Lan Zhang; 7. Some nonlinear methods for studying far-from-the-money contingent claims E. Fournié, J. M. Lasry and P.-L. Lions; 8. Stochastic volatility models E. Fournié, J. M. Lasry and N. Touzi; 9. Dynamic optimisation for a mixed portfolio with transaction costs Agnès Sulem; 10. Imperfect markets and backward stochastic differential equations N. El Karoui and M. C. Quenez; 11. Numerical methods for backward stochastic differential equations D. Chevance; 12. Viscosity solutions and numerical schemes for investment/consumption models with transaction costs Agnès Tourin and Thaleia Zariphopoulou; 13. Does volatility jump or just diffuse? A statistical approach Renzo G. Avesani and Pierre Bertrand; 14. Martingale-based hedge error control Peter Bossaerts and Bas Werker; 15. The use of second order stochastic dominance to bound European call prices: theory and results Claude Henin and Nathalie Pistre.

Editorial Reviews

Review of the hardback: '… the book can be strongly recommended to economists, probabilists, and applied mathematics working in finance.' European Mathematical Society

From the Publisher