Model Risk for European Stock Index Options

In empirical modeling, there have been two strands for pricing in the options literature, namely the parametric and nonparametric models. Often, the support for the nonparametric methods is based on a benchmark such as theBlack-Scholes model with constant volatility. In this paper, we examine the best performing parametric models against nonparametric alternatives. In particular, we study the stochastic volatility (SV) and stochastic volatility randomjump (SVJ) models as parametric benchmarks against feedforward network (FNN) models, a class of neural network models. Our choice for FNN models is due to their well-studied universal approximation property of an unknown function and its partial derivatives. Since the partial derivatives of an optionpricing formula are risk pricing tools, an accurate estimation of the unknown option pricing function is essential for pricing and hedging. Our findings indicate that FNN models offer themselves as robust option pricing tools over theirsophisticated parametric counterparts in predictive settings.