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Non-Gaussian Closed Form Solutions for Geometric Average Asian Options in the Framework of Non-Extensive Statistical Mechanics

by Pan Zhao 1,2,*, Benda Zhou 1,2 and Jixia Wang 3
1
College of Finance and Mathematics, West Anhui University, Lu’an 237012, China
2
Financial Risk Intelligent Control and Prevention Institute of West Anhui University, Lu’an 237012, China
3
School of Mathematics and Information Sciences, Henan Normal University, Xinxiang 453002, China
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(1), 71; https://doi.org/10.3390/e20010071
Received: 17 November 2017 / Revised: 30 December 2017 / Accepted: 16 January 2018 / Published: 18 January 2018
(This article belongs to the Special Issue Nonadditive Entropies and Complex Systems)
In this paper we consider pricing problems of the geometric average Asian options under a non-Gaussian model, in which the underlying stock price is driven by a process based on non-extensive statistical mechanics. The model can describe the peak and fat tail characteristics of returns. Thus, the description of underlying asset price and the pricing of options are more accurate. Moreover, using the martingale method, we obtain closed form solutions for geometric average Asian options. Furthermore, the numerical analysis shows that the model can avoid underestimating risks relative to the Black-Scholes model. View Full-Text
Keywords: geometric average Asian option; Non-extensive statistics; martingale method geometric average Asian option; Non-extensive statistics; martingale method
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Zhao, P.; Zhou, B.; Wang, J. Non-Gaussian Closed Form Solutions for Geometric Average Asian Options in the Framework of Non-Extensive Statistical Mechanics. Entropy 2018, 20, 71.

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