Options pricing with time changed Lévy processes under imprecise information

• Published in: Fuzzy optimization and decision making Vol. 14; no. 1; pp. 97 - 119
• Main Authors: Feng, Zhi-Yuan, Cheng, Johnson T.-S., Liu, Yu-Hong, Jiang, I-Ming
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.03.2015; Springer Nature B.V
• Subjects: Accounting; American dollar; Analysis; Artificial Intelligence; Brownian motion; Calculus of Variations and Optimal Control; Optimization; Decision making; Foreign exchange rates; Fuzzy; Fuzzy logic; Fuzzy set theory; Fuzzy sets; Interest rates; Kurtosis; Mathematical Logic and Foundations; Mathematical models; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Pricing; Probability Theory and Stochastic Processes; Put & call options; Random variables; Securities prices; Set theory; Skewness; Stochasticity; Studies; Treasury bills; Volatility; Stochastic volatility; Imprecise information; Fuzzy measure; Triangle-type fuzzy Number; Lévy processes
• ISSN: 1568-4539; 1573-2908
• DOI: 10.1007/s10700-014-9191-3

This study evaluates a time changed Lévy 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 Lévy model has better fitting performance when compared with the time changed Lévy and the Black and Scholes model when using S&P 500 index option data.