Numerical Methods in Finance

Numerical Methods in Finance

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Description

Numerical Methods in Finance has emerged as a discipline at the intersection of probability theory, finance and numerical analysis. This book, based on lectures given at the Newton Institute as part of a broader programme, describes a wide variety of numerical methods used in financial analysis: computation of option prices, especially of 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. Articles have been written in a pedagogic style and made reasonably self-contained, covering both mathematical matters and practical issues in numerical problems. Thus the book has something to offer economists, probabilists and applied mathematicians working in finance.show more

Product details

  • Online resource
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • English
  • 20 b/w illus. 15 tables
  • 1139173057
  • 9781139173056

Review quote

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

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. Fournie, J. M. Lasry and P.-L. Lions; 8. Stochastic volatility models E. Fournie, J. M. Lasry and N. Touzi; 9. Dynamic optimisation for a mixed portfolio with transaction costs Agnes 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 Agnes 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.show more