The Implied Volatility Skew of Single Stock Options and the Predictability of Jumps - Robustness Analysis

Sammanfattning: In this thesis, we try to understand whether the observed implied volatility skew of single stock options is significantly related to the probability of observing future return jumps in the underlying single stock. In particular, our main aim is to verify whether the skew-jump relationship persists during normal periods without any pre-scheduled information disclosure event or it is confined to earnings announcement periods. Using S&P 100 daily stock and option data from January 1996 to December 2017, we model the statistical relationship between ex-ante skew and ex-post jump using a probit model. To ensure robustness, we define skew in two ways as the difference between out-of-the-money (OTM) implied volatility and at-the-money (ATM) or in-the-money (ITM) implied volatility. We find that the statistical significance of the skew-jump relationship is preserved during normal periods with no earnings announcement: more positive put skews are related to a higher probability of observing future negative jumps and more negative call OTM-ATM skews are related to a higher probability of observing future positive jumps, both in the full period and the normal period. To improve the robustness, we repeat our analysis raising the probability threshold for jump identification and we find that while the statistical relationships do not change, the predictive accuracy improves.