方差互换的Delta
The Delta of a Variance Swap
- UNC Charlotte Department of Mathematics and Statistics（北卡罗来纳大学夏洛特分校数学与统计系）
- UBS（瑞银集团）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文定义方差互换Delta，用Carr-Madan公式分析其对标的资产价格的敏感性，证明纯货币性微笑下总Delta为零，并提出修改微笑曲线以解决该问题。
AI中文摘要：
我们将方差互换的Delta定义为方差价格对标的资产价格变化的敏感性。当隐含波动率微笑曲线可能依赖于标的资产价格时，我们使用Carr-Madan展开公式来分析这种敏感性。我们证明，对于微笑曲线是（对数）货币性的纯函数这一类别，方差互换的总Delta为零，这与市场下跌时方差上升的经验观察相悖。我们提出对微笑曲线进行简单修改以纠正此问题。
英文摘要：
We define the variance swap delta as the sensitivity of the price of variance to a change in underlying price. We use Carr-Madan spanning formulas to analyze this sensitivity when the implied volatility smile curve may depend on the underlying price. We show that the variance swap total delta is zero for the class of smile curves that are pure functions of (log) moneyness, which goes against the empirical observation that variance is up when the market is down. We propose a simple modification of the smile to correct this issue.
