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

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  • Xavier Calmet
  • Nathaniel Wiesendanger Shaw

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.

Suggested Citation

  • Xavier Calmet & Nathaniel Wiesendanger Shaw, 2020. "An analytical perturbative solution to the Merton–Garman model using symmetries," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(1), pages 3-22, January.
    • Handle: RePEc:wly:jfutmk:v:40:y:2020:i:1:p:3-22
    DOI: 10.1002/fut.22061
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