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

Lai, Choi-Hong (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

## 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 |
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Additional Information: | [1] Chapter 10, in Part III: Numerical Treatment of Nonlinear Black-Scholes equations. |

Uncontrolled Keywords: | option pricing, financial modelling, algorithm, Laplace transform, non-linear Black-Scholes equation |

Subjects: | H Social Sciences > HG Finance Q Science > QA Mathematics |

School / Department / Research Groups: | School of Computing & Mathematical Sciences School of Computing & Mathematical Sciences > Centre for Numerical Modelling & Process Analysis School of Computing & Mathematical Sciences > Centre for Numerical Modelling & Process Analysis > Computational Science & Engineering Group School of Computing & Mathematical Sciences > Department of Mathematical Sciences |

Related URLs: | |

Last Modified: | 25 Jul 2012 12:46 |

URI: | http://gala.gre.ac.uk/id/eprint/1268 |

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