An analytical perturbative solution to the Merton Garman model using symmetries
Pricing of Securities
2021-01-14 v2 Mathematical Finance
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.
Keywords
Cite
@article{arxiv.1909.01413,
title = {An analytical perturbative solution to the Merton Garman model using symmetries},
author = {Xavier Calmet and Nathaniel Wiesendanger Shaw},
journal= {arXiv preprint arXiv:1909.01413},
year = {2021}
}