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arXiv · 1909.01413

An analytical perturbative solution to the Merton Garman model using symmetries

Xavier Calmet·Nathaniel Wiesendanger Shaw
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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.

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Xavier Calmet, Nathaniel Wiesendanger Shaw. 2019-09-03. An analytical perturbative solution to the Merton Garman model using symmetries. https://arxiv.org/abs/1909.01413

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