Leveraged ETF Options Implied Volatility Paradox: A Statistical Study

SFB 649 Discussion Paper 2016-004, Economic Risk, Berlin

42 Pages Posted: 27 Jun 2016 Last revised: 14 Nov 2016

See all articles by Wolfgang K. Härdle

Wolfgang K. Härdle

Humboldt University of Berlin - Institute for Statistics and Econometrics; Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Sergey Nasekin

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Zhiwu Hong

Xiamen University - Wang Yanan Institute for Studies in Economics (WISE)

Date Written: November 13, 2016

Abstract

In this paper, we study the statistical properties of the moneyness scaling transformation by Leung and Sircar (2015). This transformation adjusts the moneyness coordinate of the implied volatility smile in an attempt to remove the discrepancy between the IV smiles for levered and unlevered ETF options. We construct bootstrap uniform confidence bands which indicate that there remains a possibility that the implied volatility smiles are still not the same, even after moneyness scaling has been performed. This presents possible arbitrage opportunities on the (L)ETF market which can be exploited by traders. An empirical data application shows that there are indeed such opportunities in the market which result in risk-free gains for the investor. A dynamic "trade-with-the-smile" strategy based on a dynamic semiparametric factor model is presented. This strategy utilizes the dynamic structure of implied volatility surface allowing out-of-sample forecasting and information on unleveraged ETF options to construct theoretical one-step-ahead implied volatility surfaces. Additionally, we propose a semi-analytic and a simulation-based estimation approach for incorporating stochastic volatility into the moneyness scaling method. This approach allows to infer the "expected integrated variance smile" from the data.

Keywords: exchange-traded funds, options, moneyness scaling, stochastic volatility, bootstrap, dynamic factor models

JEL Classification: C00, C14, C50, C58

Suggested Citation

Härdle, Wolfgang K. and Nasekin, Sergey and Hong, Zhiwu, Leveraged ETF Options Implied Volatility Paradox: A Statistical Study (November 13, 2016). SFB 649 Discussion Paper 2016-004, Economic Risk, Berlin. Available at SSRN: https://ssrn.com/abstract=2800943 or http://dx.doi.org/10.2139/ssrn.2800943

Wolfgang K. Härdle (Contact Author)

Humboldt University of Berlin - Institute for Statistics and Econometrics ( email )

Unter den Linden 6
Berlin, D-10099
Germany
+49 30 2093 5631 (Phone)
+49 30 2093 5649 (Fax)

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Unter den Linden 6
Berlin, D-10099
Germany

Sergey Nasekin

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE) ( email )

Spandauer Strasse 1
Berlin, D-10178
Germany

Zhiwu Hong

Xiamen University - Wang Yanan Institute for Studies in Economics (WISE) ( email )

A 307, Economics Building
Xiamen, Fujian 361005
China

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