Model Uncertainty and Pricing Performance in Option Valuation

The objective of this paper is to evaluate option pricing model performance at the cross sectional level. For this purpose, we propose a statistical framework, in which we in particular account for the uncertainty associated with the reported pricing performance. Instead of a single figure, we determine an entire probability distribution function for the loss function that is used to measure option pricing model performance. This methodology enables us to visualize the effect of parameter uncertainty on the reported pricing performance. Using a data driven approach, we confirm previous evidence that standard volatility models with clustering and leverage effects are sufficient for the option pricing purpose. In addition, we demonstrate that there is short-term persistence but long-term heterogeneity in cross-sectional option pricing information. This finding has two important implications. First, it justifies the practitioner’s routine to refrain from time series approaches, and instead estimate option pricing models on a cross-section by cross-section basis. Second, the long term heterogeneity in option prices pinpoints the importance of measuring, comparing and testing option pricing model for each cross-section separately. To our knowledge no statistical testing framework has been applied to a single cross-section of option prices before. We propose a methodology that addresses this need. The proposed framework can be applied to a broad set of models and data. In the empirical part of the paper, we show by means of example, an application that uses a discrete time volatility model on S&P 500 index options.