Characterization of Student’s T- Distribution with Some Application to Finance

Abstract

The distributional form of the returns on the underlying assets plays a key role in finance under valuation theories for derivative securities. Among them, Student t-distributions are generally applied in financial studies as heavy-tailed substitute to the normal distribution. Therefore, distributions of logarithmic asset returns can often be fitted extremely well using Student t-distribution with  degree of freedom, such that . The aim of this paper is to investigate the characterization behavior of Student t-distributions and its related properties into finance which are based on computational aspects using Mathematica. Furthermore, convolution, infinity divisibility and self-decomposability properties of Lévy-Student process are considered as background to the option pricing. Finally, applications of modeling high frequency price returns are discussed.

Keywords: Characterization behavior, degree of freedom, heavy-tail, Lévy-Student process