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

See all articles by Geng Deng

Geng Deng

Wells Fargo

Tim Dulaney

Securities and Exchange Commission

Craig J. McCann

Securities Litigation and Consulting Group

Mike Yan

Securities Litigation and Consulting Group

Date Written: January 7, 2014

Abstract

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

Suggested Citation

Deng, Geng and Dulaney, Tim and McCann, Craig J. and Yan, Mike, Crooked Volatility Smiles: Evidence from Leveraged and Inverse ETF Options (January 7, 2014). Journal of Derivatives and Hedge Funds, 19, 278-294, 2014. Available at SSRN: https://ssrn.com/abstract=2190931 or http://dx.doi.org/10.2139/ssrn.2190931

Geng Deng

Wells Fargo ( email )

1753 Pinnacle Dr
7th Floor
Mc Lean, VA Virginia 22102
United States

Tim Dulaney (Contact Author)

Securities and Exchange Commission ( email )

100 F Street, NW
Washington, DC 20549-1105
United States

Craig J. McCann

Securities Litigation and Consulting Group ( email )

3998 Fair Ridge Drive, Suite 250
Fairfax, VA 22033
United States

Mike Yan

Securities Litigation and Consulting Group ( email )

3998 Fair Ridge Drive, Suite 250
Fairfax, VA 22033
United States
7035396780 (Phone)

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