The Fitted Finite Volume and Power Penalty Methods for Option Pricing

This book contains mostly the author's up-to-date research results in the area. Option pricing has attracted much attention in the past decade from applied mathematicians, statisticians, practitioners and educators. Many partial differential equation-based theoretical models have been developed for valuing various options. These models do not have any practical use unless their solutions can be found. However, most of these models are far too complex to solve analytically and numerical approximations have to be sought in practice. The contents of the book consist of three parts: (i) basic theory of stochastic control and formulation of various option pricing models, (ii) design of finite volume, finite difference and penalty-based algorithms for solving the models and (iii) stability and convergence analysis of the algorithms. It also contains extensive numerical experiments demonstrating how these algorithms perform for practical problems. The theoretical and numerical results demonstrate these algorithms provide efficient, accurate and easy-to-implement numerical tools for financial engineers to price options.

This book is appealing to researchers in financial engineering, optimal control and operations research. Financial engineers and practitioners will also find the book helpful in practice.

Auteur
Prof. Song Wang received a Ph.D. degree from Trinity College, University of Dublin, in Numerical Analysis in 1989. He served as the Head of the Department of Mathematics & Statistics, Curtin University, during the period from 2014 to 2019. Currently, he is a Full Professor at Curtin University. His research interests include numerical solution of partial differential equations, numerical optimization and optimal control, and computational finance. He has authored and co-authored over 130 research journal papers in these areas and is on the editorial boards of several international journals and a chief editor of two international journals. Prof. Wang and his collaborators have developed many advanced algorithms for HamiltonJacobiBellman equations, optimal control and constrained optimization. He is responsible for the design and analysis of fitted finite volume and penalty methods for solving variational inequalities governing European and American option valuation, which become increasingly popular in numerical option pricing. In the past 15 years, Prof. Wang, along with their collaborators, has worked together on developing systematically finite volume and penalty methods for pricing various types of options and published numerous papers in this area. Prof. Wang has an in-depth knowledge of both computation and analysis of control and optimization problems with an emphasis on HamiltonJacobiBellman equations arising in control and financial engineering. He has been a researcher and educator and was a senior software engineer. He understands the needs from both academics and practitioners.

Contenu

1. Introduction.- 2. European options on one asset.- 3. American options on one asset.- 4. Two-factor option models.- 5. The super-convergent finite volume method for pricing options.