The respected Comrade
"The sector of basic sciences, including mathematics, physics, chemistry and biology, should, while consolidating the theoretical and methodological base for the development of science and technology, generate international-level research findings."
We have studied the time-changed mixed fractional Brownian model which represents a sub-diffusive dynamics with self-similarity and long-range dependence.
In statistical physics, a sub-diffusive process exhibits the flat periods of constant values and the heavy-tailed rests of particles. In last years, since some underlying asset dynamics reveals the periods of constant values and long-range dependence, so in option pricing, scholars have introduced the time-changed mixed fractional Brownian model to represent such behaviors.
In spite of evident abnormal behaviors such as the periods of constant values and long-range dependence, if an investor trades under mixed hedging strategy in the classical Black-Scholes model, it might bring about bad results like large hedging error ratios. Therefore, it is very important in the financial practice to find a mixed hedging strategy and an option price corresponding to above mentioned abnormality.
To date, this topic has been limited to the classical Black-Scholes model. We have derived a pricing formula for a European call option under a mixed hedging strategy in discrete time setting of the time-changed mixed fractional Brownian model. Further, through some numerical experiments and empirical analysis, we have proved that our mixed hedging is better for stock price dynamics with periods of constant values. Our results show that a stability parameter α and a Hurst index as well as a risk preference parameter μ and a fractal scalingΔt, play an important role in option pricing and portfolio hedging, in the discrete time case.
The research results have been published under the title of "Option pricing under mixed hedging strategy in time-changed mixed fractional Brownian model"(https://doi.org/10.1016/j.cam.2022.114496) in the SCI journal "Journal of computational and applied mathematics".