英文标题：
《Leveraged {ETF} implied volatilities from {ETF} dynamics》
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作者：
Tim Leung, Matthew Lorig, Andrea Pascucci
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最新提交年份：
2015
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英文摘要：
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.
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中文摘要：
埃芬奇交易基金（ETF）行业的增长导致了ETF及其杠杆交易对手{（LETFs）}的期权交易。我们研究了当标的ETF由一类一般的局部随机波动率模型建模时，ETF和LETF隐含波动率曲面之间的关系。对于收益取决于ETF和/或LETF终值的欧式期权，导出了价格的封闭形式近似值。建立了这种定价近似的严格误差界。还导出了隐含挥发率的闭合形式近似。我们还讨论了一个比较杠杆比率隐含波动率的标度程序。隐含波动率扩展和标度在三个著名的环境中进行了测试：CEV、Heston和SABR。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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