Model-Free Risk-Neutral Moments and Proxies

Zhangxin Liu, Thijs van der Heijden

Research output: Working paper

Abstract

Estimation of risk-neutral (RN) moments is of great interest to both academics and practitioners. We study 1) the model-free measure of RN moments by Bakshi, Kapadia and Madan (2003); 2) RN moments that are used in the VIX and SKEW index by the Chicago Board Options Exchange; 3) nonparametric RN moments that are calculated as the difference of implied volatilities across moneyness levels; and 4) the level, slope and curvature of the implied volatility smirk. More specifically, we investigate the estimation procedure by examining the consequence of directly using raw option data versus applying various smoothing methods to the option data. In the simulation study, we study estimation errors arise from integration truncation, discreteness of strike prices and asymmetric truncation. We show that applying smoothing methods reduces the estimation errors of true moments but the size and direction of estimation errors are largely unquantifiable. In the empirical study, we find that applying smoothing methods increases the Kendall and Spearman rank correlations among RN moment estimates. We conduct a case study that examines the relationship between RN skewness and future realised stock returns from 1996 to 2014. We show that a strategy that is to long the quintile portfolio with the lowest RN skewness stocks yields a negative and significant Fama-French Five-Factor alpha. This finding is robust across all RN skewness measures.
Original languageEnglish
Publication statusPublished - 4 Jul 2016

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Estimation error
Skewness
Smoothing
Implied volatility
Factors
Volatility index
Empirical study
Stock returns
Curvature
Exchange option
Measure of risk
Rank correlation
Simulation study

Cite this

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title = "Model-Free Risk-Neutral Moments and Proxies",
abstract = "Estimation of risk-neutral (RN) moments is of great interest to both academics and practitioners. We study 1) the model-free measure of RN moments by Bakshi, Kapadia and Madan (2003); 2) RN moments that are used in the VIX and SKEW index by the Chicago Board Options Exchange; 3) nonparametric RN moments that are calculated as the difference of implied volatilities across moneyness levels; and 4) the level, slope and curvature of the implied volatility smirk. More specifically, we investigate the estimation procedure by examining the consequence of directly using raw option data versus applying various smoothing methods to the option data. In the simulation study, we study estimation errors arise from integration truncation, discreteness of strike prices and asymmetric truncation. We show that applying smoothing methods reduces the estimation errors of true moments but the size and direction of estimation errors are largely unquantifiable. In the empirical study, we find that applying smoothing methods increases the Kendall and Spearman rank correlations among RN moment estimates. We conduct a case study that examines the relationship between RN skewness and future realised stock returns from 1996 to 2014. We show that a strategy that is to long the quintile portfolio with the lowest RN skewness stocks yields a negative and significant Fama-French Five-Factor alpha. This finding is robust across all RN skewness measures.",
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Model-Free Risk-Neutral Moments and Proxies. / Liu, Zhangxin; van der Heijden, Thijs.

2016.

Research output: Working paper

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N2 - Estimation of risk-neutral (RN) moments is of great interest to both academics and practitioners. We study 1) the model-free measure of RN moments by Bakshi, Kapadia and Madan (2003); 2) RN moments that are used in the VIX and SKEW index by the Chicago Board Options Exchange; 3) nonparametric RN moments that are calculated as the difference of implied volatilities across moneyness levels; and 4) the level, slope and curvature of the implied volatility smirk. More specifically, we investigate the estimation procedure by examining the consequence of directly using raw option data versus applying various smoothing methods to the option data. In the simulation study, we study estimation errors arise from integration truncation, discreteness of strike prices and asymmetric truncation. We show that applying smoothing methods reduces the estimation errors of true moments but the size and direction of estimation errors are largely unquantifiable. In the empirical study, we find that applying smoothing methods increases the Kendall and Spearman rank correlations among RN moment estimates. We conduct a case study that examines the relationship between RN skewness and future realised stock returns from 1996 to 2014. We show that a strategy that is to long the quintile portfolio with the lowest RN skewness stocks yields a negative and significant Fama-French Five-Factor alpha. This finding is robust across all RN skewness measures.

AB - Estimation of risk-neutral (RN) moments is of great interest to both academics and practitioners. We study 1) the model-free measure of RN moments by Bakshi, Kapadia and Madan (2003); 2) RN moments that are used in the VIX and SKEW index by the Chicago Board Options Exchange; 3) nonparametric RN moments that are calculated as the difference of implied volatilities across moneyness levels; and 4) the level, slope and curvature of the implied volatility smirk. More specifically, we investigate the estimation procedure by examining the consequence of directly using raw option data versus applying various smoothing methods to the option data. In the simulation study, we study estimation errors arise from integration truncation, discreteness of strike prices and asymmetric truncation. We show that applying smoothing methods reduces the estimation errors of true moments but the size and direction of estimation errors are largely unquantifiable. In the empirical study, we find that applying smoothing methods increases the Kendall and Spearman rank correlations among RN moment estimates. We conduct a case study that examines the relationship between RN skewness and future realised stock returns from 1996 to 2014. We show that a strategy that is to long the quintile portfolio with the lowest RN skewness stocks yields a negative and significant Fama-French Five-Factor alpha. This finding is robust across all RN skewness measures.

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Liu Z, van der Heijden T. Model-Free Risk-Neutral Moments and Proxies. 2016 Jul 4.