Author(s)

F. Mostafa & T. Dillon

Abstract

In this paper the pricing performance of the artificial neural network is compared to the Black-Scholes and the GARCH option-pricing model. The artificial neural network is trained on the implied volatility rather then the option price, which leads to an improved performance when compared to the competing models. The hedging performance of the neural network, GARCH option-pricing model and the Black-Scholes are also analysed. Keywords: neural networks, option pricing, hedging, implied volatility, GARCH option pricing model. 1 Introduction Since the publication of the Black-Scholes model in 1973 (Black and Scholes [1]), it remains the most quoted scientific paper in the world. The model made a key contribution to option trading, where investors are able to calculate a fair value of an option contract. This model had its limitations, which stem from the unrealistic assumptions. The Black-Scholes behaviour has been well documented in literature (Henderson [2]). The most interesting stylised fact of the Black- Scholes model that has captured the attention of researches and practitioners alike is the volatility skew (or volatility smile). This stylised fact can be seen when the implied volatility is backed out from the Black-Scholes formula and is plotted with respect to the option moneyness. The graph deviated from a flat line, which is a contradiction to the constant volatility assumption of the Black- Scholes. Researchers then turned to more sophisticated methods for option valuation using stochastic volatility models (Ritchken and Trevor [3], Peter and Kris [4], Engle and Mustafa [5], Duan [6] and Heston et al. [7]). The GARCH option pricing model (GOPM) introduced by Duan [6] is based on a discrete-time

Keywords

neural networks, option pricing, hedging, implied volatility, GARCH option pricing model.