Implied Volatility of Leveraged ETF Options

25 Pages Posted: 20 Oct 2012 Last revised: 26 Oct 2015

See all articles by Tim Leung

Tim Leung

University of Washington - Department of Applied Math

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering

Date Written: September 25, 2014

Abstract

This paper studies the problem of understanding implied volatilities from options written on leveraged exchanged-traded funds (LETFs), with an emphasis on the relations between LETF options with different leverage ratios. We first examine from empirical data the implied volatility skews for LETF options based on the S&P 500. In order to enhance their comparison with non-leveraged ETFs, we introduce the concept of moneyness scaling and provide a new formula that links option implied volatilities between leveraged and unleveraged ETFs. Under a multiscale stochastic volatility framework, we apply asymptotic techniques to derive an approximation for both the LETF option price and implied volatility. The approximation formula reflects the role of the leverage ratio, and thus allows us to link implied volatilities of options on an ETF and its leveraged counterparts. We apply our result to quantify matches and mismatches in the level and slope of the implied volatility skews for various LETF options using data from the underlying ETF option prices. This reveals some apparent biases in the leverage implied by the market prices of different products, long and short with leverage ratios two times and three times.

Keywords: exchange-traded funds, leverage, implied volatility, stochastic volatility, moneyness scaling

JEL Classification: G12, G13, G17

Suggested Citation

Leung, Tim and Sircar, Ronnie, Implied Volatility of Leveraged ETF Options (September 25, 2014). Applied Mathematical Finance, vol. 22, issue 2, pp.162-188, 2015. Available at SSRN: https://ssrn.com/abstract=2164518 or http://dx.doi.org/10.2139/ssrn.2164518

Tim Leung (Contact Author)

University of Washington - Department of Applied Math ( email )

Lewis Hall 217
Department of Applied Math
Seattle, WA 98195
United States
9253381749 (Phone)

HOME PAGE: http://faculty.washington.edu/timleung/

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering ( email )

Princeton, NJ 08544
United States

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