An analytical perturbative solution to the Merton–Garman model using symmetries. Issue 1 (29th September 2019)

• Record Type: Journal Article
• Authors: Calmet, Xavier; Wiesendanger Shaw, Nathaniel
• Is Part Of: Journal of futures markets. Volume 40:Issue 1(2020)
• Page Start: 3
• Page End: 22
• Publication Date: 2019-09-29
• Subjects: Merton–Garman model -- option pricing model -- perturbation theory; Commodity exchanges -- Periodicals; Foreign exchange futures -- Periodicals; 332.632
• DOI: 10.1002/fut.22061
• Languages: English
• ISSNs: 0270-7314

Abstract

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.