An analytical perturbative solution to the Merton Garman model using symmetries

Xavier Calmet and Nathaniel Wiesendanger Shaw

Papers from arXiv.org

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.

Date: 2019-09, Revised 2021-01
New Economics Papers: this item is included in nep-cmp
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Published in J Futures Markets, 40, 3-22 (2020)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1909.01413

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