Numerical Methods in Finance

doi:10.1017/CBO9781139173056

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.

Review of the hardback:‘… the book can be strongly recommended to economists, probabilists, and applied mathematics working in finance.’

Source: European Mathematical Society

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Contributors
pp vii-viii
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Introduction
pp ix-x
- By L.C.R. Rogers, University of Bath, D. Talay
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Convergence of Numerical Schemes for Degenerate Parabolic Equations Arising in Finance Theory
pp 1-21
- By G. Barles, Université de Tours, Pare de Grandmont
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Continuous-Time Monte Carlo Methods and Variance Reduction
pp 22-42
- By Nigel J. Newton, University of Essex
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Recent Advances in Numerical Methods for Pricing Derivative Securities
pp 43-66
- By M. Broadie, Columbia University, J. Detemple, McGill University
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American Options: A Comparison of Numerical Methods
pp 67-87
- By F. AitSahlia, P. Carr, Cornell University, Ithaca
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Fast, Accurate and Inelegant Valuation of American Options
pp 88-92
- By Adriaan Joubert, Queen Mary & Westfield College, Mile End Road, L.C.G. Rogers, University of Bath
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Valuation of American Option in a Jump-diffusion Models
pp 93-114
- By Xiao Lan Zhang
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Some Nonlinear Methods for Studying Far-from-the-money Contingent Claims
pp 115-145
- By E. Fournié, J.M. Lasry, P.L. Lions, Université Paris Dauphine
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Monte Carlo Methods for Stochastic Volatility Models
pp 146-164
- By E. Fournié, J. M. Lasry, N. Touzi, Université Paris Dauphine
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Dynamic Optimization for a Mixed Portfolio with Transaction Costs
pp 165-180
- By Agnès Sulem
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Imperfect Markets and Backward Stochastic Differential Equations
pp 181-214
- By N. El Karoui, Université de Paris, M.C. Quenez, Université de Marne la Vallée
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Reflected Backward SDEs and American Options
pp 215-231
- By N. El Karoui, Université de Paris, E. Pardoux, Université de Provence, M.C. Quenez, Université de Marne la Vallée
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Numerical Methods for Backward Stochastic Differential Equations
pp 232-244
- By D. Chevance, Université d'Orleans
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Viscosity Solutions and Numerical Schemes for Investment/Consumption Models with Transaction Costs
pp 245-269
- By Agnès Tourin, Thaleia Zariphopoulou, University of Wisconsin
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Does Volatility Jump or Just Diffuse? A Statistical Approach
pp 270-289
- By Renzo G. Avesani, University of Brescia, Pierre Bertrand, Université Blaise Pascal
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Martingale-Based Hedge Error Control
pp 290-304
- By Peter Bossaerts, California Institute of Technology, Bas Werker, Tilburg University
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The Use of Second-Order Stochastic Dominance To Bound European Call Prices: Theory and Results
pp 305-326
- By Claude Henin, University of Ottawa, Nathalie Pistre
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Numerical Methods in Finance

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Contributors
pp vii-viii

Introduction
pp ix-x

Convergence of Numerical Schemes for Degenerate Parabolic Equations Arising in Finance Theory
pp 1-21

Continuous-Time Monte Carlo Methods and Variance Reduction
pp 22-42

Recent Advances in Numerical Methods for Pricing Derivative Securities
pp 43-66

American Options: A Comparison of Numerical Methods
pp 67-87

Fast, Accurate and Inelegant Valuation of American Options
pp 88-92

Valuation of American Option in a Jump-diffusion Models
pp 93-114

Some Nonlinear Methods for Studying Far-from-the-money Contingent Claims
pp 115-145

Monte Carlo Methods for Stochastic Volatility Models
pp 146-164

Dynamic Optimization for a Mixed Portfolio with Transaction Costs
pp 165-180

Imperfect Markets and Backward Stochastic Differential Equations
pp 181-214

Reflected Backward SDEs and American Options
pp 215-231

Numerical Methods for Backward Stochastic Differential Equations
pp 232-244

Viscosity Solutions and Numerical Schemes for Investment/Consumption Models with Transaction Costs
pp 245-269

Does Volatility Jump or Just Diffuse? A Statistical Approach
pp 270-289

Martingale-Based Hedge Error Control
pp 290-304

The Use of Second-Order Stochastic Dominance To Bound European Call Prices: Theory and Results
pp 305-326

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