Model-Free Risk-Neutral Moments and Proxies

64 Pages Posted: 10 Aug 2015 Last revised: 6 Jul 2016

See all articles by Zhangxin (Frank) Liu

Zhangxin (Frank) Liu

The University of Western Australia Business School

Thijs van der Heijden

University of Melbourne - Department of Finance; Financial Research Network (FIRN)

Date Written: July 4, 2016


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.

Keywords: Risk-Neutral Moments, Skewness, Kurtosis, Implied Volatility Smirk, Skew, Curvature, VIX

JEL Classification: G11, G12

Suggested Citation

Liu, Zhangxin (Frank) and van der Heijden, Thijs, Model-Free Risk-Neutral Moments and Proxies (July 4, 2016). Available at SSRN: or

Zhangxin (Frank) Liu (Contact Author)

The University of Western Australia Business School ( email )

School of Business
35 Stirling Highway
Crawley, Western Australia 6009

Thijs Van der Heijden

University of Melbourne - Department of Finance ( email )

198 Berkeley Street
Carlton VIC 3010

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane


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