The application of nonlinear fuzzy parameters PDE method in pricing and hedging European options

In recent years, fuzzy sets theory has been introduced as a means of modeling the uncertainties of the input parameters of the Black-Scholes-Merton European options pricing formula. However, some standard assumptions underlying the Black-Scholes-Merton model including those of constant interest rate and volatility no longer hold in fuzzy environments. Therefore, it is inappropriate to price options with uncertain parameters based on the Black-Scholes-Merton formula. In this paper, we propose a methodology for option pricing under fuzzy environments which is essentially different from the Black-Scholes-Merton option pricing framework. We build a nonlinear fuzzy-parameter PDE model for obtaining the fuzzy option prices and we develop dominating optimal hedging strategies under fuzzy environments which provide valuable insights for risk management and trading in financial markets.