Tempered Fractional Lévy Processes and Option Pricing

Abstract

Tempered Fractional Lévy Processes incorporating lookback times in forming asset price drifts along with rates of mean reversion to these drifts are employed in studying option markets. The processes have already been observed to deliver perpetually high levels of excess kurtosis in fast reverting markets to highly stochastic drifts using low lookback times. These features are quite characteristic of stock price markets. The results on option data are the opposite with long lookback times and slow rates of mean reversion. The option market features could reflect the effects of a relatively smaller collection of more sophisticated players along with lower trading frequencies compared to the underlying stock markets.

Keywords: Bilateral Gamma Process, Excess Kurtosis, Fast Fourier Transform

JEL Classification: G10, G11, G12