英文文献：Stochastic Volatility-随机波动率
英文文献作者：Torben G. Andersen,Luca Benzoni
英文文献摘要：
We give an overview of a broad class of models designed to capture stochastic volatility in financial markets, with illustrations of the scope of application of these models to practical finance problems. In a broad sense, this model class includes GARCH, but we focus on a narrower set of specifications in which volatility follows its own random process and is therefore a latent factor. These stochastic volatility specifications fit naturally in the continuous-time finance paradigm, and therefore serve as a prominent tool for a wide range of pricing and hedging applications. Moreover, the continuous-time paradigm of financial economics is naturally linked with the theory of volatility modeling and forecasting, and in particular with the practice of constructing ex-post volatility measures from high-frequency intraday data (realized volatility). One drawback is that in this setting volatility is not measurable with respect to observable information, and this feature complicates estimation and inference. Further, the presence of an additional state variable|volatility|renders the model less tractable from an analytic perspective. New estimation methods, combined with model restrictions that allow for closed-form solutions, make it possible to address these challenges while keeping the model consistent with the main properties of the data.

我们概述了一大类用于捕捉金融市场随机波动的模型，并说明了这些模型在实际金融问题中的应用范围。从广义上讲，这个模型类包括GARCH，但是我们关注的是更窄的规范集，其中波动遵循它自己的随机过程，因此是一个潜在的因素。这些随机波动率规范自然符合连续时间金融范式，因此成为广泛定价和对冲应用的突出工具。此外，金融经济学的连续时间范式自然与波动率建模和预测理论联系在一起，特别是与从高频盘中数据(已实现波动率)构建事后波动率度量的实践联系在一起。一个缺点是，在这种情况下，波动率不能根据可观察信息进行测量，这一特性使估计和推断变得复杂。此外，附加的状态变量|的波动性|使模型从分析的角度变得更难以处理。新的评估方法，加上允许封闭形式解决方案的模型限制，使得在保持模型与数据的主要属性一致的同时解决这些挑战成为可能。