A european call options pricing model using the infinite pure jump levy process in a fuzzy environment

Abstract

An options pricing model is a pricing model in a real‐life environment and needs to take into account uncertainties in the environment such as randomness and fuzziness. As such, this paper makes use of fuzzy theory to construct an options pricing model based on an infinite pure jump Levy process in a fuzzy environment, with the drift, diffusion, and jump as trapezoidal fuzzy random variables. Following this, the Monte Carlo simulation algorithm is used to conduct numerical simulations, where the instrumental variable method is employed to increase the convergence rate of the simulation. A simulation experiment is also used to compare the pricing result of the Black–Scholes (BS) model, the variance gamma (VG) options pricing model in a certain environment, and the VG options pricing model in a fuzzy environment. The result of the analysis indicates that the VG options pricing model in a fuzzy environment is a feasible one, with the fuzzy interval narrowing as the option exercise price increases. On the other hand, the fuzzy interval widens as the option expiration date increases. Owing to the introduction of more uncertainties, the option price obtained under this model is higher than those of other models. The option price under the model is also more sensitive to changes in the jump parameter: as the jump parameter increases, the fuzzy interval narrows. Finally, an empirical examination using Tencent Holdings (HK.0700) and its stock options indicates that the expectation using fuzzy pricing is closer to the market price than that of the BS model. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.