Options pricing with time changed Lévy processes under imprecise information

Abstract

This study evaluates a time changed Levy model for European call options under a fuzzy environment. The proposed model is characterized by high frequency jumps, stochastic volatility, and stochastic volatility with the jumps, existing in the returns process of financial assets. Moreover, to consider imperfect and unpredictable accounting information, this study uses fuzzy logic to account for the impreciseness of the accounting information, which can not be described in extant models, and provides reasonable reference instruments for future research on option pricing under a jump diffusion model with imprecise market information. Our empirical results also show that the fuzzy time changed Levy model has better fitting performance when compared with the time changed Levy and the Black and Scholes model when using S&P 500 index option data.