Pricing of financial derivatives based on the Tsallis statistical theory

Asset return distributions usually have peaks, fat tails and skewed tails, because of the impact of extreme events outside financial markets. The Tsallis distribution has the peak and fat-tail characteristic, and the asymmetric jump process can fit the skewed tail of returns. Therefore, to accurately describe asset returns, we propose a price model by the use of the Tsallis distribution and a Poisson jump process, which can characterize the long-term memory and the skewness of asset returns. Moreover, using the stochastic differential theory and the martingale method, we obtain an explicit solution for pricing European options. (C) 2020 Published by Elsevier Ltd.

Automated summary

The paper proposes a price model using the Tsallis distribution and a Poisson jump process to accurately describe the long-term memory and skewness of asset returns, and obtains an explicit solution for pricing European options using stochastic differential theory and the martingale method.