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Nonparametric Estimation of Fractional Option Pricing Model

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  • Qing Li
  • Songlin Liu
  • Misi Zhou

Abstract

The establishment of the fractional Black–Scholes option pricing model is under a major condition with the normal distribution for the state price density (SPD) function. However, the fractional Brownian motion is deemed to not be martingale with a long memory effect of the underlying asset, so that the estimation of the state price density (SPD) function is far from simple. This paper proposes a convenient approach to get the fractional option pricing model by changing variables. Further, the option price is transformed as the integral function of the cumulative density function (CDF), so it is not necessary to estimate the distribution function individually by complex approaches. Finally, it encourages to estimate the fractional option pricing model by the way of nonparametric regression and makes empirical analysis with the traded 50 ETF option data in Shanghai Stock Exchange (SSE).

Suggested Citation

  • Qing Li & Songlin Liu & Misi Zhou, 2020. "Nonparametric Estimation of Fractional Option Pricing Model," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-8, December.
    • Handle: RePEc:hin:jnlmpe:8858821
    DOI: 10.1155/2020/8858821
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    Cited by:

    1. Vasile Brătian & Ana-Maria Acu & Camelia Oprean-Stan & Emil Dinga & Gabriela-Mariana Ionescu, 2021. "Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion," Mathematics, MDPI, vol. 9(22), pages 1-20, November.

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