Publication details

A multifractional option pricing formula

Authors

ARANEDA Axel A.

Year of publication 2024
Type Article in Periodical
Magazine / Source FLUCTUATION AND NOISE LETTERS
MU Faculty or unit

Faculty of Economics and Administration

Citation
web https://www.worldscientific.com/doi/epdf/10.1142/S0219477524500603
Doi http://dx.doi.org/10.1142/S0219477524500603
Keywords Multifractional Brownian motion; Hurst exponent; long-range dependence; European option pricing
Description 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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