方差、离散度和相关互换

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摘要翻译：
近年来，银行出售了最坏期权、珠峰期权和喜马拉雅期权等结构性产品，导致短期相关风险敞口。因此，他们开始有兴趣抵消这种风险的一部分，即回购相关性。这种策略有两种方式：纯相关掉期或分散交易，在指数期权中持有头寸，在成份股期权中持有相反头寸。这些分散交易是使用看涨、看跌、跨界、方差掉期以及第三代波动率产品建立的。当考虑使用方差掉期的离散度交易时，人们立即看到它给出了相关风险敞口。实证分析表明，这种隐含的相关性并不等于同期限的相关性互换的达成。本文旨在从理论上解释这种传播。事实上，我们证明了一个离散交易的P&L等于隐含的和实现的相关性之间的价差乘以各组成部分的平均方差和波动性部分的总和。此外，这个波动部分是二阶的，更准确地说，是伏尔加阶的。因此，所观察到的相关扩散完全可以用离散交易的伏尔加解释。当考虑分散交易的不同加权方案时，将对这一结果进行审查。
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英文标题：
《Variance dispersion and correlation swaps》
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作者：
Antoine Jacquier and Saad Slaoui
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最新提交年份：
2010
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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英文摘要：
  In the recent years, banks have sold structured products such as worst-of options, Everest and Himalayas, resulting in a short correlation exposure. They have hence become interested in offsetting part of this exposure, namely buying back correlation. Two ways have been proposed for such a strategy : either pure correlation swaps or dispersion trades, taking position in an index option and the opposite position in the components options. These dispersion trades have been set up using calls, puts, straddles, variance swaps as well as third generation volatility products. When considering a dispersion trade using variance swaps, one immediately sees that it gives a correlation exposure. Empirical analysis have showed that this implied correlation was not equal to the strike of a correlation swap with the same maturity. The purpose of this paper is to theoretically explain such a spread. In fact, we prove that the P&L of a dispersion trade is equal to the sum of the spread between implied and realised correlation - multiplied by an average variance of the components - and a volatility part. Furthermore, this volatility part is of second order, and, more precisely, is of volga order. Thus the observed correlation spread can be totally explained by the volga of the dispersion trade. This result is to be reviewed when considering different weighting schemes for the dispersion trade.
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PDF链接：
https://arxiv.org/pdf/1004.0125

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关键词：Quantitative correlation Considering Theoretical derivatives 交易 been 期权 dispersion 头寸