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

Author

Listed:
  • Kittisak Chumpong

    (Division of Computational Science, Faculty of Science, Prince of Songkla University, Songkhla 90110, Thailand
    Mathematics and Statistics with Applications Research Center, Prince of Songkla University, Songkhla 90110, Thailand
    Financial Mathematics, Data Science and Computational Innovations Research Unit (FDC), Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, 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
    Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand)

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.

Suggested Citation

  • Kittisak Chumpong & Khamron Mekchay & Fukiat Nualsri & Phiraphat Sutthimat, 2024. "Closed-Form Formula for the Conditional Moment-Generating Function Under a Regime-Switching, Nonlinear Drift CEV Process, with Applications to Option Pricing," Mathematics, MDPI, vol. 12(17), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2667-:d:1465337
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    References listed on IDEAS

    as
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