Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

SFB649DP2016 004

Leveraged ETF options implied volatility paradox: a statistical study

Wolfgang Karl Härdle
Sergey Nasekin
Zhiwu Hong

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 in a statistical sense 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. We build possible arbitrage strategies by constructing portfolios with LETF shares and options which possibly have a positive value at the point of creation and non-negative value at the expiration time. 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. The codes used to obtain the results in this paper, are available on

exchange-traded funds, options, moneyness scaling, arbitrage, bootstrap, dynamic factor models

JEL Classification:
C00, C14, C50, C58