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The pricing and numerical analysis of lookback options for mixed fractional Brownian motion

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  • Chen, Qisheng
  • Zhang, Qian
  • Liu, Chuan

Abstract

Using the stochastic differential equation driven by the composite Poisson process of mixed fractional Brownian motion, the price model of a mixed jump-diffusion fractional Brownian motion environment is established. Under the condition of Merton’s assumption, the Cauchy initial value problem of stochastic differential equations is iterated. The method is estimated, and the Merton formula of the European put option under the mixed jump-diffusion model is obtained, and the call-back option and the bearish option pricing formula of the mixed jump-diffusion fractional Brownian motion European floating strike price are given.

Suggested Citation

  • Chen, Qisheng & Zhang, Qian & Liu, Chuan, 2019. "The pricing and numerical analysis of lookback options for mixed fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 123-128.
    • Handle: RePEc:eee:chsofr:v:128:y:2019:i:c:p:123-128
    DOI: 10.1016/j.chaos.2019.07.038
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    References listed on IDEAS

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    1. Li, Yulin, 2003. "A martingale inequality and large deviations," Statistics & Probability Letters, Elsevier, vol. 62(3), pages 317-321, April.
    2. Lesigne, Emmanuel & Volný, Dalibor, 2001. "Large deviations for martingales," Stochastic Processes and their Applications, Elsevier, vol. 96(1), pages 143-159, November.
    3. Michel Crouhy & Dan Galai, 2018. "Are Banks Special?," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 8(04), pages 1-19, December.
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    Cited by:

    1. Deng, Guohe, 2020. "Pricing perpetual American floating strike lookback option under multiscale stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Ma, Pengcheng & Najafi, Alireza & Gomez-Aguilar, J.F., 2024. "Sub mixed fractional Brownian motion and its application to finance," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    3. Liu, Zhibin & Huang, Shan, 2021. "Carbon option price forecasting based on modified fractional Brownian motion optimized by GARCH model in carbon emission trading," The North American Journal of Economics and Finance, Elsevier, vol. 55(C).
    4. Shi, Gang & Gao, Jinwu, 2021. "European Option Pricing Problems with Fractional Uncertain Processes," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    5. Wang, Jian & Yan, Yan & Chen, Wenbing & Shao, Wei & Wang, Jian & Tang, Weiwei, 2021. "Equity-linked securities option pricing by fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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