Abstract We propose a methodology to use functional factors in empirical asset pricing models. We establish conditions under which it is possible to recover linear beta pricing. The proposed estimation approach allows us to use high-dimensional functional curves, such as the term structure of interest rates or the implied volatility smile, as factors. This framework enables the estimation of functional factor loadings as well as risk premium parameters of factor models. We derive estimation algorithms and establish the asymptotic consistency and normality of the parameter estimates. In an empirical application, we show that the implied variance smile of the S&P500 is a potential pricing factor for momentum-sorted portfolios. In particular, a positive risk premium is earned by the convexity of the implied variance curve.

中文翻译：

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具有功能因素的经验资产定价

摘要 我们提出了一种在经验资产定价模型中使用功能因素的方法。我们建立了可以恢复线性贝塔定价的条件。所提出的估计方法允许我们使用高维函数曲线，例如利率期限结构或隐含波动率微笑作为因子。该框架能够估计功能因子载荷以及因子模型的风险溢价参数。我们推导出估计算法并建立参数估计的渐近一致性和正态性。在实证应用中，我们表明 S&P500 的隐含方差微笑是动量排序投资组合的潜在定价因素。特别是，隐含方差曲线的凸性会获得正的风险溢价。