Crooked Volatility Smiles: Evidence from Leveraged and Inverse ETF Options
Journal of Derivatives and Hedge Funds, 19, 278-294, 2014
23 Pages Posted: 18 Dec 2012 Last revised: 29 Apr 2017
Date Written: January 7, 2014
We find that the leverage factors of leveraged and inverse exchange traded funds can effect the "crookedness"' of volatility smiles. We model leveraged and inverse ETF option prices using partial differential equations (PDEs) and determine closed-form solutions for the option values following the method of Lipton (2001). We study a sextet of leveraged and inverse ETFs based on the S&P 500. We show that the Heston model can reproduce the crooked smiles observed in the the market price of options on leveraged and inverse leveraged exchange traded funds. By analyzing the asymptotic behavior for the implied variances at extreme strikes, we observe an approximate symmetry between pairs of LETF smiles empirically consistent with the predictions of the Heston model.
Keywords: Volatility Smile, Volatility Skew, Leveraged ETF, Inverse ETF, Options
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