LEVERAGED ETF IMPLIED VOLATILITIES FROM ETF DYNAMICS. (19th May 2016)

• Record Type: Journal Article
• Authors: Leung, Tim; Lorig, Matthew; Pascucci, Andrea
• Is Part Of: Mathematical finance. Volume 27:Number 4(2017:Oct.)
• Page Start: 1035
• Page End: 1068
• Publication Date: 2016-05-19
• Subjects: implied volatility -- local‐stochastic volatility -- leveraged exchange‐traded fund -- implied volatility scaling; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12128
• Languages: English
• ISSNs: 0960-1627

Abstract

Abstract: The growth of the exchange‐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 payoffs depend 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 settings: Heston, limited constant elasticity of variance (CEV), and limited SABR; the last two are regularized versions of the well‐known CEV and SABR models.