A multifractional option pricing formula

被引：2
作者：
Araneda, Axel A. [1 ]
机构：
[1] Masaryk Univ, Inst Financial Complex Syst, Dept Finance, Brno, Czech Republic
来源：
FLUCTUATION AND NOISE LETTERS | 2024年 / 23卷 / 06期
关键词：
Multifractional Brownian motion; Hurst exponent; long-range dependence; European option pricing; BROWNIAN-MOTION; DEPENDENCE; MEMORY;
D O I：
10.1142/S0219477524500603
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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页数：11
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