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

Author

Listed:
  • Hainaut, Donatien

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Leonenko, Nikolai

    (Cardiff University)

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.

Suggested Citation

  • Hainaut, Donatien & Leonenko, Nikolai, 2020. "Option pricing in illiquid markets: a fractional jump-diffusion approach," LIDAM Reprints ISBA 2020007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2020007
    DOI: https://doi.org/10.1016/j.cam.2020.112995
    Note: In : Journal of computational and applied mathematics - Vol. 381 (1/1/2021)
    as

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