Abstract
This paper is dedicated to the study of the geometric average Asian call option pricing under non-extensive statistical mechanics for a time-varying coefficient diffusion model. We employed the non-extensive Tsallis entropy distribution, which can describe the leptokurtosis and fat-tail characteristics of returns, to model the motion of the underlying asset price. Considering that economic variables change over time, we allowed the drift and diffusion terms in our model to be time-varying functions. We used the formula, Feynman–Kac formula, and ansatz to obtain a closed-form solution of geometric average Asian option pricing with a paying dividend yield for a time-varying model. Moreover, the simulation study shows that the results obtained by our method fit the simulation data better than that of Zhao et al. From the analysis of real data, we identify the best value for q which can fit the real stock data, and the result shows that investors underestimate the risk using the Black–Scholes model compared to our model.
Highlights
In financial markets, the movement of asset price is the foundation of the pricing of financial assets and derivatives
Wang [2] studied the Black–Scholes stock option pricing model based on dynamic investment strategy, deriving new option pricing models based on the Black–Scholes option pricing theory
Considering that the return distribution of the underlying stock has a peak and fat tails in actual financial markets, in this study, we used the non-extensive Tsallis entropy distribution with long-term interaction and historical memory characteristics to replace the normal distribution without historical memory and modeled the motion of the underlying asset price
Summary
The movement of asset price is the foundation of the pricing of financial assets and derivatives. Considering that the return distribution of the underlying stock has a peak and fat tails in actual financial markets, in this study, we used the non-extensive Tsallis entropy distribution with long-term interaction and historical memory characteristics to replace the normal distribution without historical memory and modeled the motion of the underlying asset price. This model can depict the leptokurtosis and fat-tail characteristics of the distribution of returns. A simulation study shows that our method can better fit the simulation data than that of Zhao et al [30]
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