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Risk Evaluating for Subdiffusive Option Price Model with Gamma Subordinator

In: Mathematical and Statistical Methods for Actuarial Sciences and Finance

Author

Listed:
  • Nataliya Shchestyuk

    (Orebro University, School of Business
    National University of Kyiv-Mohyla Academy, Department of Mathematics)

  • Svitlana Drin

    (Orebro University, School of Business
    National University of Kyiv-Mohyla Academy, Department of Mathematics)

  • Serhii Tyshchenko

    (National University of Kyiv-Mohyla Academy, Department of Mathematics)

Abstract

The article focuses on Value-at-risk measuring for options in situations characterized by the lack of liquidity when the underlying stock price has motionless periods. A similar behavior can be observed in physical systems exhibiting sub-diffusion. In the considered sub-diffusive model, the bond movement and stock process are time-changed by the stochastic clock with gamma subordinator. In the model, the two techniques for option pricing were considered. The first very common approach for the time-changed model is to find option prices as the discounted expected payoff under the risk-neutral measure. The second technique for option pricing is based on a fractional version of what is called Dupire’s equation. The Value-at-Risk evaluating procedure for the proposed model was discussed and we show that this procedure is based on the Fractional Fokker-Planck equation (FFPE).

Suggested Citation

  • Nataliya Shchestyuk & Svitlana Drin & Serhii Tyshchenko, 2024. "Risk Evaluating for Subdiffusive Option Price Model with Gamma Subordinator," Springer Books, in: Marco Corazza & Frédéric Gannon & Florence Legros & Claudio Pizzi & Vincent Touzé (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, pages 286-291, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-64273-9_47
    DOI: 10.1007/978-3-031-64273-9_47
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