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.
An Option Pricing Model Using High Frequency Data
