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arXiv · 2303.16314

A multifractional option pricing formula

Axel A. Araneda
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Abstract

Fractional Brownian motion has become a standard tool to address long-range dependence in financial time series. However, a constant memory parameter is too restrictive to address different market conditions. Here we model the price fluctuations using a multifractional Brownian motion assuming that the Hurst exponent is a time-deterministic function. Through the multifractional Ito calculus, both the related transition density function and the analytical European Call option pricing formula are obtained. The empirical performance of the multifractional Black-Scholes model is tested by calibration of option market quotes for the SPX index and offers best fit than its counterparts based on standard and fractional Brownian motions.

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Axel A. Araneda. 2024-06-01. A multifractional option pricing formula. https://doi.org/10.1142/s0219477524500603

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