Fitted Finite Volume and Power Penalty Methods for Option Pricing

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 Hamilton–Jacobi–Bellman 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 Hamilton–Jacobi–Bellman 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.

“It is intended not only for specialists working in this scientific field but also for that part of the ‘academic audience’ that has to go its way from university education to serious scientific excellence! … The monograph is exclusively professionally written and the materials are presented in an attractive way.” (Nikolay Kyurkchiev, zbMATH 1458.91008, 2021)

• 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.