Abstract
This thesis consists of three essays on options. Essay 1 (Chapter 2) is an empirical study on the early exercise premium (EEP) of American options with evidence from OEX and XEO options. Essay 2 (Chapter 3) is a theoretical and numerical exploration of the rare disaster concern index (RIX). Essay 3 (Chapter 4) is an empirical study of RIX in the U.S. energy stock options market. The empirical and theoretical analyses presented in this thesis contribute to the understanding of option pricing, risk-neutral measures, and financial market dynamics.
In Chapter 2, the price discrepancy between American and European options is examined using the S&P 100 index options (OEX and XEO, respectively), providing a direct comparison under identical market conditions. The findings reveal that EEP is not only a function of early exercise rights but is also significantly influenced by liquidity constraints. Moreover, the results show that implied volatility differences between American and European options encapsulate various risk components beyond the standard volatility framework.
Chapter 3 introduces the RIX as a measure of higher-order risks. An enhanced definition of RIX and its exact model based on the Gram-Charlier density are illustrated, refining the measurement of extreme downside risks beyond traditional moment-based estimators and bridging the gap between the theoretical framework and empirical application of RIX.
In Chapter 4, the predictive power of RIX is empirically tested in the U.S. energy stock options market, a sector particularly susceptible to geopolitical and macroeconomic shocks. The results indicate that firms with higher pre-event RIX levels experience significantly larger cumulative abnormal returns (CAR) around earnings announcements and major economic events. Furthermore, the predictive strength of RIX is amplified during periods of heightened market uncertainty, demonstrating its robustness as a tail risk indicator.