Leveraged {ETF} implied volatilities from {ETF} dynamics

Tim Leung, Matthew Lorig and Andrea Pascucci

Papers from arXiv.org

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.

Date: 2014-04, Revised 2015-04
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Citations: View citations in EconPapers (13)

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