A new application of fuzzy set theory to the Black–Scholes option pricing model

A jump-diffusion model for option pricing under fuzzy environments

“…Yoshida (2003) and Yoshida et al (2006) discussed the valuation of European and American options with uncertainty for both randomness and fuzziness in the output variables, by introducing fuzzy logic to the stochastic financial model. Lee et al (2005) adopted the fuzzy decision theory and Bayes' rule for measuring fuzziness in the practice of option analysis. Wu (2004Wu ( , 2005Wu ( , 2007 obtained the so called fuzzy pattern of the Black-Scholes formula in his papers when the arithmetics in the (conventional) Black-Scholes formula are replaced by fuzzy arithmetic.…”

Calibrating parametric exponential Lévy models to option market data by incorporating statistical moments priors

“…In contrast, option pricing models with jumps such as Lévy processes are able to reproduce such features of option prices traded in real market (Gatheral, 2006). Nonparametric approaches (Han & Lee, 2008;Huang, 2008;Ko, 2009;Lee, Tzeng, & Wang, 2005;Zhang, Xiao, & He, 2009), which do not rely on pre-assumed models but instead try to uncover/induce the model, have also been proposed to price European options. However, they have some inherent problems in directly pricing path-dependent exotic options since they have no underlying asset dynamics, while the Lévy processes make it possible to generate paths of underlying assets because of their intrinsic dynamics, thereby directly pricing any path-dependent derivatives.…”

Fuzzy Levy-GJR-GARCH American Option Pricing Model Based on an Infinite Pure Jump Process

“…Regarding the application of fuzzy theory in option pricing, Cheng-Few Lee et al (2005) [19] were among the first to incorporate fuzzy decision space in investor decision making, deriving a B-S model under a fuzzy environment. Their research demonstrates that models that fail to incorporate fuzzy numbers tend to underestimate the values of call options.…”