Fuzzy Option Pricing for Jump Diffusion Model using Neuro Volatility Models

Recently there has been a growing interest in studying fuzzy option pricing using Monte Carlo (MC) methods for diffusion models. The traditional volatility estimator has a larger asymptotic variance. In this paper, data-driven neurovolatility estimates with smaller variances are used to obtain direct volatility forecasts. Asymmetric nonlinear adaptive fuzzy numbers are used to address ambiguity and vagueness associated with volatility estimates. This study uses fuzzy set theory and data-driven volatility forecasts to study call option prices of the S&P 500 index. Four modeling approaches have been considered, Black-Scholes (BS) model, Monte Carlo option pricing with normal / t errors, and the Jump-Diffusion (JD) model. Fuzzy acuts of option prices are presented and discussed under different parameter values. Our experimental study suggests that the JD model predicts the call option price more accurately compared to BS, normal errors, and t errors using the volatility estimate obtained using the Bayesian approach.