Estimation of risk premia from option data and using machine learning methods: comparison, forecast quality and potential of hybrid strategies

根据风险溢价的时间序列特性和交易资产的横截面来解释风险溢价，是金融经济学的核心。虽然基本资产定价方程清楚地说明了风险补偿的经济学--决定风险溢价的是资产收益和随机贴现系数的协方差--但这一一般概念的经验实现具有挑战性，并继续推动金融领域的理论和计量经济学研究。在一部浩瀚而活跃的文学作品中，人们可以区分两种策略。第一种是以理论为基础的结构模型进行实证分析，其优点是基于原则性的经济思想。然而，对经验绩效的评估往往受到错综复杂的模型结构的阻碍，这些结构排除了使用标准计量经济学方法的可能性。此外，所采用的模型有时高度程式化，依赖于明显不切实际的假设。第二种策略包括经验主义的方法，这些方法在计量经济学上更容易获得，但容易受到没有理论的衡量的批评，以及无节制地寻找风险因素。结合法兰克福大学和图宾根大学的两个金融研究小组的力量，这个项目更仔细地研究了两个衡量风险溢价的新框架，这两个框架可以被认为是基于理论的策略和经验策略的极端案例。第一个是前瞻性的，因为它利用了反映在期权价格中的市场预期。它是基于理论的，因为它依赖于对基本资产定价公式的重新表述。这一策略的非参数性质反驳了使用不切实际假设的批评。第二种方法使用机器学习方法，因此在某种意义上是向后看的，这些方法在历史数据中寻找模式。人们不是依靠经济理论，而是依靠数据科学的概念。虽然它们的理念从根本上不同，但两个新框架关注的是同一个利益对象，即反映在金融资产的有条件预期收益中的风险溢价。这一共同目标使这两种在方法上互不相交的方法具有可比性，原则上是可以结合的。因此，我们的提案旨在对这两个框架的预测性能进行比较评估--回顾条件预期是均方误差最优预测--以及开发和评估结合金融理论和基于数据科学的方法的混合框架。由于对量化模型的局限性缺乏更深入的了解是最近金融危机的主要驱动力之一，我们强调需要对基于期权和基于数据科学的框架以及待开发的混合模型的可能性和局限性提出批判性观点。

The explanation of risk premia, in terms of their time series properties and in the cross-section of traded assets, is at the heart of financial economics. While the fundamental asset pricing equation makes a clear statement about the economics of risk compensation - it is the covariance of an asset's return and the stochastic discount factor that determines the risk premium - empirical implementations of this general concept are challenging and continue to spur theoretical and econometric research in finance. Within a vast and active literature one can distinguish two strategies. The first employs theory-based structural models for their empirical analysis, which has the advantage of being based on principled economic thought. However, the assessment of the empirical performance is often hampered by intricate model structures that preclude the use of standard econometric methods. Moreover, the models employed are sometimes highly stylized and rely on apparently unrealistic assumptions. The second strategy consists of empirical approaches that are econometrically more accessible, but are prone to the critique of measurement without theory and an undisciplined fishing for risk factors. Joining the forces of two finance research groups at the Universities of Frankfurt and Tübingen, this project takes a closer look at two novel frameworks to measure risk premia that can be conceived of as extreme cases of the theory-based and the empirical strategies. The first is forward-looking, because it exploits market expectations that are reflected in option prices. It is theory-based, because it relies on a reformulation of the fundamental asset pricing equation. The non-parametric nature of this strategy counters the critique of employing unrealistic assumptions. The second approach employs machine learning methods and is thus backward-looking in a sense that these methods look for patterns in historical data. One does not draw on economic theory, but concepts from data science. While their philosophies are fundamentally different, the two new frameworks are concerned with the same object of interest, namely the risk premium reflected in the conditional expected return of a financial asset. This common objective makes the two methodologically disjoint approaches comparable, and in principle combinable. Accordingly, our proposal aims at providing a comparative evaluation of the two frameworks in terms of their forecast performance - recalling that the conditional expectation is the mean-squared-error optimal forecast - and the development and assessment of hybrid frameworks that combine the financial theory- and data science-based approaches. Because a lack of deeper understanding of the limits of quantitative models was one main driver of the recent financial crises, we emphasize the need to provide a critical view on the possibilities and limitations of the option-based and the data science-based framework, as well as the hybrid models to be developed.