Predictive accuracy of option pricing models considering high-frequency data

Abstract

Purpose: Recently, considerable attention has been given to forecasting, not only the mean and the variance, but also the entire probability density function (pdf) of the underlying asset. These forecasts can be obtained as implied moments of future distribution originating from European call and put options. However, the predictive accuracy of option pricing models is not so well established. With this in mind, this research aims to identify the model that predicts the entire pdf most accurately when compared to the ex-post “true” density given by high-frequency data at expiration date. Methodology: The methodological part includes two steps. In the first step, several probability density functions are estimated using different option pricing models, considering the values of major market indices with different maturities. These implied probability density functions are risk neutral. In the second step, the implied pdfs are compared against the “true” density obtained from the high-frequency data to examine which one gives the best fit out-of-sample. Results: The results support the idea that a “true” density function, although unknown, can be estimated by employing the kernel estimator within high-frequency data and adjusted for risk preferences. Conclusion: The main conclusion is that the Shimko model outperforms the Mixture Log-Normal model as well as the Edgeworth expansion model in terms of out-of-sample forecasting accuracy. This study contributes to the existing body of research by: i) establishing the benchmark of the “true” density function using high-frequency data, ii) determining the predictive accuracy of the option pricing models and iii) providing applicative results both for market participants and public authorities.

Keywords

• option pricing models
• high-frequency data
• kernel estimation
• benchmark density function
• predictive accuracy