Implied Volatility of Leveraged ETF Options
Implied Volatility of Leveraged ETF Options
复制标题
杠杆ETF期权的隐含波动率
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
R. Sircar
中科院分区：
文献类型：
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作者：
Tim Leung;R. Sircar
摘要本文研究了杠杆交易基金（LETF）期权隐含波动率的理解问题，重点研究了不同杠杆率的LETF期权之间的关系。首先，我们从经验数据中检查基于标准普尔500指数的LETF期权的隐含波动率偏差。为了加强与非杠杆ETF的比较，我们引入了货币规模的概念，并提供了一个新的公式，连接杠杆和非杠杆ETF之间的期权隐含波动率。在一个多尺度随机波动率框架下，我们应用渐近技术得到一个近似的LETF期权价格和隐含波动率。近似公式反映了杠杆比率的作用，因此我们可以将ETF期权的隐含波动率与其杠杆期权联系起来。我们应用我们的研究结果来量化匹配和不匹配的水平和斜率的隐含波动率偏差的各种LETF期权使用的数据从相关的ETF期权价格。这揭示了不同产品的市场价格所隐含的杠杆率存在明显的偏差，无论是杠杆率为两倍还是三倍的多头产品还是空头产品。
Abstract This paper studies the problem of understanding implied volatilities from options written on leveraged exchanged-traded funds (LETFs), with an emphasis on the relations between LETF options with different leverage ratios. We first examine from empirical data the implied volatility skews for LETF options based on the S&P 500. In order to enhance their comparison with non-leveraged ETFs, we introduce the concept of moneyness scaling and provide a new formula that links option implied volatilities between leveraged and unleveraged ETFs. Under a multiscale stochastic volatility framework, we apply asymptotic techniques to derive an approximation for both the LETF option price and implied volatility. The approximation formula reflects the role of the leverage ratio, and thus allows us to link implied volatilities of options on an ETF and its leveraged counterparts. We apply our result to quantify matches and mismatches in the level and slope of the implied volatility skews for various LETF options using data from the underlying ETF option prices. This reveals some apparent biases in the leverage implied by the market prices of different products, long and short with leverage ratios two times and three times.