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Fractional Order Stochastic Differential Equation with Application in European Option Pricing

Author

Listed:
  • Qing Li
  • Yanli Zhou
  • Xinquan Zhao
  • Xiangyu Ge

Abstract

Memory effect is an important phenomenon in financial systems, and a number of research works have been carried out to study the long memory in the financial markets. In recent years, fractional order ordinary differential equation is used as an effective instrument for describing the memory effect in complex systems. In this paper, we establish a fractional order stochastic differential equation (FSDE) model to describe the effect of trend memory in financial pricing. We, then, derive a European option pricing formula based on the FSDE model and prove the existence of the trend memory (i.e., the mean value function) in the option pricing formula when the Hurst index is between 0.5 and 1. In addition, we make a comparison analysis between our proposed model, the classic Black-Scholes model, and the stochastic model with fractional Brownian motion. Numerical results suggest that our model leads to more accurate and lower standard deviation in the empirical study.

Suggested Citation

  • Qing Li & Yanli Zhou & Xinquan Zhao & Xiangyu Ge, 2014. "Fractional Order Stochastic Differential Equation with Application in European Option Pricing," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-12, August.
    • Handle: RePEc:hin:jnddns:621895
    DOI: 10.1155/2014/621895
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    Cited by:

    1. Benabdallah Mohsine & Hiderah Kamal, 2018. "Strong rate of convergence for the Euler–Maruyama approximation of one-dimensional stochastic differential equations involving the local time at point zero," Monte Carlo Methods and Applications, De Gruyter, vol. 24(4), pages 249-262, December.
    2. Chen, Weihao & Liu, Yansheng & Zhao, Daliang, 2024. "Approximate controllability for a class of stochastic impulsive evolution system with infinite delay involving the fractional substantial derivative," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    3. Din Prathumwan & Wannika Sawangtong & Panumart Sawangtong, 2017. "An Analysis on the Fractional Asset Flow Differential Equations," Mathematics, MDPI, vol. 5(2), pages 1-17, June.

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