Fuzzy Option Pricing Using a Novel Data-Driven Feed Forward Neural Network Volatility Model

Recently there has been a growing interest in combining randomness and fuzziness to solve option pricing problems in finance using volatility models such as GARCH (generalized autoregressive conditional heteroskedasticity) and Heston-Nandi GARCH. The possibility theory for fuzzy option pricing (for real option, European option and binary option) has been demonstrated in the literature by fuzzifying the parameters such as volatility. However, many fuzzy option pricing approaches remain difficult to use with real data. A neural network (NN) is a highly parameterized model, widely promoted as a universal approximator such that with enough data it could learn any smooth predictive relationship. In this paper we first introduce a novel data-driven feed forward NN predictive model for conditional variance and demonstrate the superiority of the proposed model for option pricing over other volatility models. Using the NN predictive model, two different fuzzy estimates of the sensitivity measure vega (ν, which measures the dependence of option price on volatility σ) are proposed. We use different estimates of the sensitivity measure and compute the α-cuts of the fuzzy call price.