LEVERAGED ETF IMPLIED VOLATILITIES FROM ETF DYNAMICS
研究了ETF和杠杆ETF隐含波动率曲面的关系，推导出欧式期权定价和隐含波动率的闭式近似，并在Heston、CEV和SABR模型下验证，对衍生品交易员和量化研究者有参考价值。
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.