A multifractional option pricing formula
| Authors | |
|---|---|
| Year of publication | 2024 |
| Type | Article in Periodical |
| Magazine / Source | FLUCTUATION AND NOISE LETTERS |
| MU Faculty or unit | |
| 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. |