Pricing Variance Swaps under MRG Model with Regime-Switching: Discrete Observations Case

Anqi Zou, Jiajie Wang () and Chiye Wu ()
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Anqi Zou: School of Information Science and Technology, Jinan University, Guangzhou 510632, China
Jiajie Wang: Shenzhen Campus, Jinan University, Shenzhen 518053, China
Chiye Wu: Shenzhen Campus, Jinan University, Shenzhen 518053, China

Mathematics, 2023, vol. 11, issue 12, 1-30

Abstract: In this paper, we creatively price the discretely sampled variance swaps under the mean-reverting Gaussian model (MRG model in short) with regime-switching asymmetric double exponential jump diffusion. We extend the traditional MRG model by further considering the trend of the financial market as well as a sudden and unexpected event of the market. This new model is meaningful because it uses observable Markov chains that represent market states to adjust its parameters, which helps capture the movement of the market and fluctuations in asset prices. By utilizing the characteristic function and the conditional transition characteristic function, we obtain analytical solutions for pricing formulae. Note that this is our first effort to provide the analytical solution for the ordinary differential equations satisfied by the Feynman–Kac theorem. To achieve this, we have developed a new methodology in Proposition 2 that involves dividing the sampling interval into more detailed switching and non-switching intervals. One significant advantage of our closed-form solution is its high computational accuracy and efficiency. Subsequent semi-Monte Carlo simulations will provide specific validation results.

Keywords: variance swaps; mean-reverting Gaussian model; double exponential jump-diffusion; discrete sampling; characteristic function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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