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An analytical perturbative solution to the Merton Garman model using symmetries
Version 2 2023-06-07, 08:28
Version 1 2023-06-07, 06:44
journal contribution
posted on 2023-06-07, 08:28 authored by Xavier CalmetXavier Calmet, Nathaniel Wiesendanger ShawIn 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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Publication status
- Published
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- Published version
Journal
Journal of Futures MarketsISSN
0270-7314Publisher
WileyExternal DOI
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1Volume
40Page range
3-22Department affiliated with
- Accounting and Finance Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2019-09-11First Open Access (FOA) Date
2019-11-25First Compliant Deposit (FCD) Date
2019-09-02Usage metrics
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