Computational Modeling of Non-Gaussian Option Price Using Non-extensive Tsallis’ Entropy Framework

• Published in: Computational economics Vol. 57; no. 4; pp. 1353 - 1371
• Main Authors: Nayak, Gangadhar, Singh, Amit Kumar, Senapati, Dilip
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2021; Springer Nature B.V
• Subjects: Algorithms; Behavioral/Experimental Economics; Computer Appl. in Social and Behavioral Sciences; Computer science; Datasets; Distribution functions; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Economics and Finance; Electronic trading systems; Empirical analysis; Entropy; High frequency trading; Math Applications in Computer Science; Normal distribution; Normalization; Operations Research/Decision Theory; Probability distribution; Securities markets; Stock prices; Cubic power-law behavior; Tsallis entropy; Generalized JS measure; CCDF; lognormal distribution
• ISSN: 0927-7099; 1572-9974
• DOI: 10.1007/s10614-020-10015-3

Financial markets have always been subject to various risk constraints which are necessary for better market prediction and accurate pricing. In this context, we derive stock price distribution subject to first and second moment constraints along with the normalization constraint in terms of the q -lognormal distribution. The derived distribution is validated against six high-frequency empirical datasets. To characterize the extreme fluctuation of empirical stock returns, we derive an analytical expression for complementary cumulative distribution function of the q -Gaussian distribution in terms of Hypergeometric2 F 1 function. However, for the computation of the non-extensive parameter ‘ q ’, we provide a precise algorithm. The estimated value of ‘ q ’ clearly describes the well-known stylized facts such as tail fluctuation, non-Gaussian intra-day returns, and cubic power-law behavior. As the option price depends on the underlying dynamics of the stock price, we derive a accurate and closed expression for option price using q -lognormal distribution.