We document the phenomenon that average excess returns of out-of-the-money puts and calls on bond futures are negative, both unconditionally and conditionally on economic states. To explain these findings, we develop economically motivated restrictions in the context of a theory in which the pricing kernel is a general diffusion process with spanned and unspanned components. Our reconciliation is a framework that introduces market incompleteness and priced unspanned volatility risks, allowing for time-varying downside and upside futures risk premiums. The estimated model shows consistency with data on bond yields, yield volatilities, bond futures return volatilities, option prices, and option risk premiums.

中文翻译：

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国债期权回报和具有未跨越风险的模型

我们记录了这样一种现象：债券期货的价外看跌期权和看涨期权的平均超额收益无论是无条件还是有条件地对经济状态都是负的。为了解释这些发现，我们在定价内核是具有跨度和非跨度组件的一般扩散过程的理论背景下制定了经济动机的限制。我们的调节框架引入了市场不完整性和定价的波动性风险，允许随时间变化的下行和上行期货风险溢价。估计模型与债券收益率、收益率波动性、债券期货收益波动性、期权价格和期权风险溢价的数据保持一致。