Leveraged ETF Implied Volatilities from ETF Dynamics
Mathematical Finance, Forthcoming
32 Pages Posted: 28 Apr 2014 Last revised: 16 Dec 2015
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
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