Risk-Neutral Density Extraction from Option Prices: Improved Pricing with Mixture Density Networks

One of the central goals in finance is to find better models for pricing and hedging financial derivatives such as call and put options. We present a new semi-nonparametric approach to risk-neutral density extraction from option prices which is based on an extension of the concept of mixture density networks. The central idea is to model the shape of the risk-neutral density in a flexible, nonlinear way as a function of the time horizon. Thereby, stylized facts such as negative skewness and excess kurtosis are captured. The approach is applied to a very large set of intraday options data on the FTSE 100 recorded at LIFFE. It is shown to yield significantly better results in terms of out-of-sample pricing accuracy in comparison to the basic and an extended Black-Scholes model. It is also significantly better than a more elaborate GARCH option pricing model which includes a time-dependent volatility process. From the perspective of risk management, the extracted risk-neutral densities provide valuable information for Value-at-Risk estimations. Index Terms--Hedging, mixture density networks, options, pricing, risk-neutral densities.