Numerical Methods in Finance

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

• ISBN13: 9780521573542
• ISBN10: 0521573548
• Format: Hardcover
• Copyright: 1997-06-28
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Contributors	vii	(2)
Introdution	ix
G. Barles
Convergence of Numerical Schemes for Degenerate Parabolic Equation Arising in Finance Theory	1	(21)
Nigel J. Newton
Continous--Time Monte Carlo Methods and Variance Reduction	22	(21)
M. Broadie
J. Detemple
Recent Advances in Numerical Methods for Pricing Derivative Securities	43	(24)
F. AitSahlia
P. Carr
American Options: A Comparison of Numerical Methods	67	(21)
Adriaan Joubert
L. C. G. Rogers
Fast, Accurate and Intelegant Valuantion of American Options	22	(5)
Xiao Lan Zhang
Valuation of American Option in a Jump-diffusion Models	93	(22)
E. Fournie
J. M. Lasry
P. L. Lions
Some Nonlinear Methods for Studying Far-Form-the-money Contingent Claims	115	(31)
E. Fournie
J. M. Lasry
N. Touzi
Monte Carlo Methods for Stochastic Volatility Models	146	(19)
Agnes Sulem
Dynamic Optimization for a Mixed Portfolio with Transaction Cost	165	(16)
N. EI Karoui
M. C. Quenez
Imperfect Markets and Backward Stochastic Differential Equations	181	(34)
N. EI Karoui
E. Pardoux
M. C. Quenez
Reflected Backward SDEs and American Options	215	(17)
D. Chevance
Numerical Methods for Backward Stochastic Differential Equations	232	(13)
Agnes Tourin
Thaleia Zariphopoulou
Viscosity Solutions and Numerical Schemes for Investment/Consumption Models with Transaction Costs	245	(25)
Renzo G. Avesani
Pierre Bertrand
Does Volantility Jump or Just Diffuse? A Statistical approach	270	(20)
Peter Bossaerts
Bas Werker
Martingale--Based Hedge Error Control	290	(15)
Claude Henin
Nathalie Pistre
The Use of Second-Order Stochastic Dominance To Bound European Call Prices: Theory and Results	305