Option Pricing with Anomalous Scaling and Infinite-State Switching Volatility

Abstract

Volatility clustering, long-range dependence, non-Gaussianity and anomalous scaling are all well-known stylized facts of financial assets return dynamics. These elements have a relevant impact on the aptness of models for the pricing of options written on financial assets. We make us of a model developed in physics that captures the previously cited returns features. The model allows deriving closed form equations for option pricing. We present the model providing a financial interpretation of its components and discuss the parameters estimation. We then derive pricing equations and use them in an empirical application based on a major equity index option dataset.

Keywords: option pricing, anomalous scaling, Markov switching, GARCH

JEL Classification: C58, G13, C22, C51, C52, C53