The difference, average risk-neutral and physical volatility, is substantial and translates into a large return premium for sellers of index options. This paper studies a general equilibrium model based on long-run risk in an effort to explain the premium. In estimating the model using data on stock returns and volatility (VIX), the model captures the premium and also the large negative correlation between shocks to volatility and stock prices. Numerical simulations verify that writers of index options earn high rates of return in equilibrium and that the return patterns are similar to that seen in the S&P 500 index options data.

中文翻译：

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波动率溢价

平均风险中性和物理波动性的差异是巨大的，并转化为指数期权卖家的巨大回报溢价。本文研究了一个基于长期风险的一般均衡模型来解释溢价。在使用股票收益和波动率 (VIX) 数据估计模型时，该模型捕捉了溢价以及波动性冲击与股票价格之间的巨大负相关性。数值模拟验证了指数期权的作者在均衡时获得了高回报率，并且回报模式与标准普尔 500 指数期权数据中看到的相似。