An analytical perturbative solution to the Merton–Garman model using symmetries

Xavier Calmet and Nathaniel Wiesendanger Shaw

Journal of Futures Markets, 2020, vol. 40, issue 1, 3-22

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 perform 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: 2020
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https://doi.org/10.1002/fut.22061

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