We propose a new method to jointly estimate volatility risk and two-tail risk price with state-dependent features. Rather than assuming a constant risk price, as in existing models, this new method estimates an extended pricing kernel with macro-state-dependent risk prices. In contrast to the widely accepted constant risk price assumption, we find that the prices for equity, volatility, positive jump, and negative jump risks are strongly dependent on economic conditions. The empirical evidence shows that this new estimation for the macro-state-dependent property adds new pricing information that existing constant risk-price models do not provide. The estimation of macro-state-dependent property has important economic implications for the underlying dynamics and derivative markets. State-dependent risk prices substantially improve the explanation of the dynamic link between the underlying and option markets, and are important factors in the option market. With the out-of-sample test, the new method provides a stable estimation of the risk price dynamics.

中文翻译：

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具有时变宏观状态相关属性的波动风险和尾部风险溢价的联合估计

我们提出了一种新方法来联合估计具有状态相关特征的波动风险和双尾风险价格。这种新方法不是像在现有模型中那样假设一个恒定的风险价格，而是使用依赖于宏观状态的风险价格来估计一个扩展的定价内核。与广泛接受的恒定风险价格假设相反，我们发现股票、波动性、正跳跃和负跳跃风险的价格强烈依赖于经济状况。经验证据表明，这种对宏观状态相关财产的新估计增加了现有恒定风险价格模型无法提供的新定价信息。宏观状态相关财产的估计对潜在动态和衍生品市场具有重要的经济意义。与状态相关的风险价格极大地改善了对标的和期权市场之间动态联系的解释，是期权市场的重要因素。通过样本外测试，新方法提供了对风险价格动态的稳定估计。