Closed-Form Formula for the Conditional Moment-Generating Function Under a Regime-Switching, Nonlinear Drift CEV Process, with Applications to Option Pricing

Kittisak Chumpong, Khamron Mekchay (), Fukiat Nualsri and Phiraphat Sutthimat
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Kittisak Chumpong: Division of Computational Science, Faculty of Science, Prince of Songkla University, Songkhla 90110, Thailand
Khamron Mekchay: Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
Fukiat Nualsri: Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
Phiraphat Sutthimat: Financial Mathematics, Data Science and Computational Innovations Research Unit (FDC), Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand

Mathematics, 2024, vol. 12, issue 17, 1-15

Abstract: An analytical derivation of the conditional moment-generating function (MGF) for a regime-switching nonlinear drift constant elasticity of variance process is established. The proposed model incorporates both regime-switching mechanisms and nonlinear drift components to better capture market phenomena such as volatility smiles and leverage effects. Regime-switching models can match the tendency of financial markets to often change their behavior abruptly and the phenomenon that the new behavior of financial variables often persists for several periods after such a change. Closed-form formulas for the MGF under various conditions, which are then applied for option pricing, are also derived. The efficacy and accuracy of the results are validated through a discrete Markov chain simulation. The results obtained from the proposed formulas completely match with those from MC simulations, while requiring significantly less computational time.

Keywords: nonlinear drift CEV process; regime switching; moment-generating function; option pricing; analytically pricing; CIR process; inverse Feller (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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