We develop a tractable equilibrium pricing model to explain observed characteristics in equity returns, VIX futures, S&P 500 options, and VIX options data based on affine jump-diffusive state dynamics and representative agents endowed with Duffie-Epstein recursive preferences. Our calibrated model replicates consumption, dividends, and asset market data, including VIX futures returns, the average implied volatilities in SPX and VIX options, and first- and higher-order moments of VIX options returns. We document a time variation in the shape of VIX-option-implied volatility and a time-varying hedging relationship between VIX and SPX options that our model both captures.

中文翻译：

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高阶巨灾保险的价格：以 VIX 期权为例

我们开发了一个易于处理的均衡定价模型，以基于仿射跳跃扩散状态动力学和具有 Duffie-Epstein 递归偏好的代表性代理来解释股票回报、VIX 期货、标准普尔 500 期权和 VIX 期权数据中观察到的特征。我们的校准模型复制了消费、股息和资产市场数据，包括 VIX 期货回报、SPX 和 VIX 期权的平均隐含波动率，以及 VIX 期权回报的一阶和高阶矩。我们记录了 VIX 期权隐含波动率形状的时间变化，以及我们的模型都捕捉到的 VIX 和 SPX 期权之间的时变对冲关系。