The Information Content of Extreme Events Implied in the Non-complete Market

This paper empirically investigates the usefulness of extreme events implied into the non-complete option market in which return generating process of underlying asset is different from that of options. The empirical results find that the information about the extreme events implied in the option market prices has more accurate forecasting power within the tail than near the first moment of realized distribution. So, we expect that the implied information of extreme jump can help to improve the back-testing performance of value at risk where it is primarily important to take account of low-probability events. Regardless of whether calibration function for density transformation is the beta-distribution or non-parametric kernel density, extreme jump provides consistently satisfactory predictions.