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Option Pricing with Anomalous Scaling and Infinite-State Switching Volatility

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.