SFB649DP2016 004
Leveraged ETF options implied volatility paradox: a statistical study
Wolfgang Karl Härdle
Sergey Nasekin
Zhiwu Hong
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 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 www.quantlet.de.
Keywords:
exchange-traded funds, options, moneyness scaling, arbitrage,
bootstrap, dynamic factor models
JEL Classification:
C00, C14, C50, C58