Numerical solutions of certain nonlinear models in European options on a distributed computing environment

Lai, Choi-Hong ORCID: 0000-0002-7558-6398 (2008) Numerical solutions of certain nonlinear models in European options on a distributed computing environment. In: Ehrhardt, Matthias, (ed.) Nonlinear Models in Mathematical Finance: New Research Trends in Option Pricing. Nova Science Publishers, Inc., Hauppauge, NY, USA, pp. 305-320. ISBN 978-1-60456-931-5

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Abstract

Financial modelling in the area of option pricing involves the understanding of the correlations between asset and movements of buy/sell in order to reduce risk in investment. Such activities depend on financial analysis tools being available to the trader with which he can make rapid and systematic evaluation of buy/sell contracts. In turn, analysis tools rely on fast numerical algorithms for the solution of financial mathematical models. There are many different financial activities apart from shares buy/sell activities. The main aim of this chapter is to discuss a distributed algorithm for the numerical solution of a European option. Both linear and non-linear cases are considered.
The algorithm is based on the concept of the Laplace transform and its numerical inverse. The scalability of the algorithm is examined. Numerical tests are used to demonstrate the effectiveness of the algorithm for financial analysis. Time dependent functions for volatility and interest rates are also discussed. Applications of the algorithm to non-linear Black-Scholes equation where the volatility and the interest rate are functions of the option value are included. Some qualitative results of the convergence behaviour of the algorithm is examined. This chapter also examines the various computational issues of the Laplace transformation method in terms of distributed computing. The idea of using a two-level temporal mesh in order to achieve distributed computation along the temporal axis is introduced. Finally, the chapter ends with some conclusions.

Item Type: Book Section [1] Chapter 10, in Part III: Numerical Treatment of Nonlinear Black-Scholes equations. option pricing, financial modelling, algorithm, Laplace transform, non-linear Black-Scholes equation H Social Sciences > HG FinanceQ Science > QA Mathematics School of Computing & Mathematical SciencesSchool of Computing & Mathematical Sciences > Centre for Numerical Modelling & Process AnalysisSchool of Computing & Mathematical Sciences > Centre for Numerical Modelling & Process Analysis > Computational Science & Engineering GroupSchool of Computing & Mathematical Sciences > Department of Mathematical Sciences Publisher 14 Oct 2016 09:03 http://gala.gre.ac.uk/id/eprint/1268