Leveraged {ETF} implied volatilities from {ETF} dynamics
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.
Cite
@article{arxiv.1404.6792,
title = {Leveraged {ETF} implied volatilities from {ETF} dynamics},
author = {Tim Leung and Matthew Lorig and Andrea Pascucci},
journal= {arXiv preprint arXiv:1404.6792},
year = {2015}
}