Risk Evaluating for Subdiffusive Option Price Model with Gamma Subordinator

Nataliya Shchestyuk (), Svitlana Drin and Serhii Tyshchenko
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Nataliya Shchestyuk: Orebro University, School of Business
Serhii Tyshchenko: National University of Kyiv-Mohyla Academy, Department of Mathematics

A chapter in Mathematical and Statistical Methods for Actuarial Sciences and Finance, 2024, pp 286-291 from Springer

Abstract: 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).

Keywords: Option pricing; subdiffusion; Value-at-risk; Gamma subordinator (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-64273-9_47

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DOI: 10.1007/978-3-031-64273-9_47

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