Truncation error treatment for the model-free implied moment estimator

Abstract

This thesis investigates the impact of truncation, that is, the complete unavailability of significantly deep-out-of-the-money option price quotes, on the implied moment estimators of Bakshi et al. (2003) and suggests a new truncation treatment method that makes truncation error, or estimation bias due to truncation, less volatile. Although previous studies have already suggested two truncation error reduction methods for model-free implied moment estimation, these methods may not be able to effectively reduce truncation error when they are used with the implied skewness or kurtosis estimators, which rely more heavily on deep-out-of-the-money option prices. Hence, we first test whether the two existing methods, specifically, the linear extrapolation method of Jiang and Tian (2005) and the domain symmetrisation method of Dennis and Mayhew (2002), can reduce truncation error effectively even when they are used in conjunction with the two higher moment estimators. The test results show that the truncation error reduction effect may be incomplete for both methods when they are used for implied skewness or kurtosis estimation. Given this result, we further investigate the relationship between truncation level and truncation error size, and then propose an alternative method of truncation error treatment, namely, domain stabilisation, based on the relationship identified. The tests on the effectiveness of domain stabilisation reveal that although this method increases the mean size of the truncation error, it also makes the size less volatile across different observations. This result implies that when our new method is employed, truncation has less impact on cross-sectional comparison and on tracking the time-series dynamics of implied moments.