The Skew-t Option Pricing Model

Abstract

This paper presents a skew-t option pricing model. It is constructed analogously to the variance gamma option pricing model proposed by [14]. This proposed skew-t model inherits the variance gamma model’s three parameters and their respective interpretations. In addition, it also has a fat-tailed, skewed distribution and infinite-activity (pure jump) stock dynamics, which is achieved through modelling the length of time intervals as stochastic. This paper has three main insights. From a theoretical perspective, a result is obtained for the correlation between the variance gamma model’s logarithm returns and its gamma stochastic variance. This result holds for the skew-t model as well, which has reciprocal gamma variance, and it provides a new way to quantify the leverage effect under each model. The focus then shifts to the numerical procedures required for estimating the skew-t model’s parameters. Finally, an empirical comparison between the skew-t, variance gamma and Black-Scholes models is conducted. The discussion links four pieces of analysis - pricing errors, pricing biases, the higher moments of the distributions and the market’s implied volatility.