An analytical perturbative solution to the Merton Garman model using symmetries

Calmet, Xavier and Shaw, Nathaniel Wiesendanger (2019) An analytical perturbative solution to the Merton Garman model using symmetries. Journal of Futures Markets. pp. 1-30. ISSN 0270-7314

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Abstract

In this paper, we introduce an analytical perturbative solution to the Merton Garman model. It is obtained by doing perturbation theory around the exact analytical solution of a model which possesses a two-dimensional Galilean symmetry. We compare our perturbative solution of the Merton Garman model to Monte Carlo simulations and find that our solutions performs surprisingly well for a wide range of parameters. We also show how to use symmetries to build option pricing models. Our results demonstrate that the concept of symmetry is important in mathematical finance.

Item Type: Article
Schools and Departments: School of Business, Management and Economics > Accounting and Finance
School of Mathematical and Physical Sciences > Physics and Astronomy
Subjects: Q Science > QC Physics
Depositing User: Amelia Redman
Date Deposited: 11 Sep 2019 10:09
Last Modified: 25 Nov 2019 14:15
URI: http://sro.sussex.ac.uk/id/eprint/85900

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