Option pricing in illiquid markets: a fractional jump-diffusion approach

Donatien Hainaut () and Nikolai Leonenko
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Donatien Hainaut: Université catholique de Louvain, LIDAM/ISBA, Belgium
Nikolai Leonenko: Cardiff University

No 2020007, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: We study the pricing of European options when the underlying stock price is illiquid. Due to the lack of trades, the sample path of such asset prices alternates between active and motionless periods that are replicable by fractional jump-diffusions. This process is obtained by changing the time-scale of a jump-diffusion by the inverse of a Lévy subordinator. We proof that option prices are solution of a forward partial differential equation in which the derivative with respect to time is replaced by a Dzerbayshan-Caputo (D-C) derivative. The form of the D-C derivative depends upon the chosen inverted Lévy subordinator. We detail this for inverted α stable and inverted Poisson subordinators. To conclude, we propose a numerical method is proposed to compute option prices for the two types of D-C derivatives.

Keywords: Dupire’s equation; Sub-diffusion; Fractional derivative; Subordinated process (search for similar items in EconPapers)
Date: 2020-05-27
Note: In : Journal of computational and applied mathematics - Vol. 381 (1/1/2021)
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2020007

DOI: 10.1016/j.cam.2020.112995

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