Book Chapter or Conference Paper Title
Tsallis and Kaniadakis Entropy Measures for Risk Neutral Densities
Faculty / School
Faculty of Computer Sciences (FCS)
Department of Mathematical Sciences
Was this content written or created while at IBA?
International Conference on Computer Aided Systems Theory
Las Palmas de Gran Canaria, Spain
19-24 February 2017
Abstract / Description
Concepts of Econophysics are usually used to solve problems related to uncertainty and nonlinear dynamics. The risk neutral probabilities play an important role in the theory of option pricing. The application of entropy in finance can be regarded as the extension of both information entropy and probability entropy. It can be an important tool in various financial issues such as risk measures, portfolio selection, option pricing and asset pricing. The classical approach of stock option pricing is based on Black-Scholes model, which relies on some restricted assumptions and contradicts with modern research in financial literature. The Black-Scholes model is governed by Geometric Brownian Motion and is based on stochastic calculus. It depends on two factors: no arbitrage, which implies the universe of risk-neutral probabilities and parameterization of risk-neutral probability by a reasonable stochastic process. Therefore, risk-neutral probabilities are vital in this framework. The Entropy Pricing Theory founded by Gulko represents an alternative approach of constructing risk-neutral probabilities without depending on stochastic calculus. Gulko applied Entropy Pricing Theory for pricing stock options and introduced an alternative framework of Black-Scholes model for pricing European stock options. In this paper we derive solutions of maximum entropy problems based on Tsallis, Weighted-Tsallis, Kaniadakis and Weighted-Kaniadakies entropies, in order to obtain risk-neutral densities.
Sheraz, M., Preda, V., & Dedu, S. (2017, February). Tsallis and Kaniadakis entropy measures for risk neutral densities. In International Conference on Computer Aided Systems Theory (pp. 55-63). Springer, Cham.
Sheraz, M., Preda, V., & Dedu, S. (2018). Tsallis and Kaniadakis Entropy Measures for Risk Neutral Densities., 10672, 55-63. https://doi.org/10.1007/978-3-319-74727-9_7