We propose a statistical methodology for jointly estimating the pricing kernel and conditional physical return densities from option prices. Pricing kernel estimates show that negative stock market returns are significantly more painful to investors in low-volatility periods. Density estimates reflect a significantly positive risk–return trade-off, suggest that Martin’s (2017) lower bound on the equity premium is violated in high-volatility periods, and provide new evidence on the variance premium’s predictive power for excess returns as well as the co-movement between higher return moments. Lastly, we show that leading macrofinance models are at odds with basic features of conditional stock market risks and risk pricing.

中文翻译：

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条件风险和定价内核

我们提出了一种统计方法，用于联合估计期权价格的定价内核和条件实物回报密度。定价核心估计显示，在低波动性时期，负股市回报对投资者来说要痛苦得多。密度估计反映了显著的正风险回报权衡，表明 Martin （2017） 在高波动性时期违反了股票溢价的下限，并提供了关于方差溢价对超额回报的预测能力以及高回报时刻之间的协同运动的新证据。最后，我们表明，领先的宏观金融模型与条件性股票市场风险和风险定价的基本特征不一致。