Leveraged ETF Implied Volatilities from ETF Dynamics

Mathematical Finance, Forthcoming

32 Pages Posted: 28 Apr 2014 Last revised: 16 Dec 2015

See all articles by Tim Leung

Tim Leung

University of Washington - Department of Applied Math

Matthew Lorig

University of Washington - Applied Mathematics

Andrea Pascucci

University of Bologna - Department of Mathematics

Date Written: April 7, 2015

Abstract

The growth of the exhange-traded fund (ETF) industry has given rise to the trading of options written on ETFs and their leveraged counterparts (LETFs). We study the relationship between the ETF and LETF implied volatility surfaces when the underlying ETF is modeled by a general class of local-stochastic volatility models. A closed-form approximation for prices is derived for European-style options whose payoff depends on the terminal value of the ETF and/or LETF. Rigorous error bounds for this pricing approximation are established. A closed-form approximation for implied volatilities is also derived. We also discuss a scaling procedure for comparing implied volatilities across leverage ratios. The implied volatility expansions and scalings are tested in three well-known settings: CEV, Heston and SABR.

Keywords: implied volatility, leveraged ETF, moneyness scaling, local stochastic volatility

Suggested Citation

Leung, Tim and Lorig, Matthew and Pascucci, Andrea, Leveraged ETF Implied Volatilities from ETF Dynamics (April 7, 2015). Mathematical Finance, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2429900 or http://dx.doi.org/10.2139/ssrn.2429900

Tim Leung

University of Washington - Department of Applied Math ( email )

Lewis Hall 217
Department of Applied Math
Seattle, WA 98195
United States

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

Matthew Lorig (Contact Author)

University of Washington - Applied Mathematics ( email )

Seattle, WA
United States

Andrea Pascucci

University of Bologna - Department of Mathematics ( email )

Piazzadi Porta San Donato, 5
Bologna, 40126
Italy

HOME PAGE: http://www.dm.unibo.it/~pascucci

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