Parametric and nonparametric regressions on spot volatility

现货波动率的参数和非参数回归

• 批准号: 1326819
• 负责人: Jia Li
• 金额: $ 25.56万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1326819&HistoricalAwards=false
• 关键词: Parametric; nonparametric; regressions; spot; volatility

This research project develops new estimation and inference tools for continuous-time semimartingale models sampled at high frequency. The semimartingale model is the most general model for asset prices that precludes arbitrage opportunities and, as a result, has been the workhorse model in modern asset pricing.The primary intellectual merit of the proposed activities is the development of new nonlinear regression methods with the latent volatility process of a semimartingale as a regressor. The volatility process measures the intrinsic variability of the semimartingale. The methods will allow researchers to investigate the statistical relationship between economic variables and the volatility process without imposing strong assumptions.The proposed activity can be divided into three sections. The first section concerns a baseline vector nonlinear regression model involving the volatility. The estimation is performed in two steps. In the first step, the latent volatility process is recovered from high frequency data in a model-free fashion, and in the second step, the regression model is estimated via the generalized methods of moments (GMM). The statistical property of this procedure is studied. These tools allow the user to explore how the volatility process drives other economic variables and to make statistically formal statements. An empirical application is included for illustrating the use of the method.The second section extends the first section by allowing the regression model to be possibly misspecified. This extension sheds light on the robustness of the estimation method in a realistic setting in which the regression model is only considered as an approximation of the true model. The analysis on misspecified models facilitates the comparison and evaluation of competing models.The third section introduces a new regression framework which can be applied to perform nonlinear projection of the sample path of a latent volatility process onto that of another volatility process. In financial applications, the method can be used to explore how volatilities of multiple assets co-vary with each other. While the motivating examples in the proposed activity are those of financial models, the methods developed in this project are valid for generic semimartingales. Besides economics and finance, semimartingales have also been used in biological, chemical, and electrical applications, where high frequency data are also available. One can hope that some of the statistical methods developed here can find applications in these fields.

本研究计画针对以高频率取样之连续时间半鞅模型，发展新的估计与推论工具。半鞅模型是排除套利机会的最一般的资产价格模型，因此，在现代资产定价中一直是主力模型，所提出的活动的主要智力价值是开发新的非线性回归方法与半鞅的潜在波动过程作为回归量。波动率过程度量了半鞅的内在变异性。该方法将允许研究人员调查经济变量和波动过程之间的统计关系，而无需强加强有力的假设。第一部分是关于一个包含波动率的基线向量非线性回归模型。估计分两步进行。在第一步中，潜波动率过程中恢复高频数据在一个无模型的方式，并在第二步中，回归模型估计通过广义矩量法（GMM）。研究了该过程的统计特性。这些工具允许用户探索波动过程如何驱动其他经济变量，并做出统计上的正式陈述。一个实证的应用程序，包括说明使用的方法。第二节扩展了第一节，允许回归模型可能被错误指定。这种扩展揭示了在现实环境中的估计方法的鲁棒性，其中回归模型仅被认为是真实模型的近似。第三部分介绍了一个新的回归框架，该框架可用于将一个潜在波动过程的样本路径非线性投影到另一个波动过程的样本路径上。在金融应用中，该方法可以用来探索多种资产的波动率如何相互协变。虽然在拟议的活动激励的例子是金融模型，在这个项目中开发的方法是有效的一般半鞅。除了经济学和金融学，半鞅还被用于生物、化学和电子应用，这些应用也可以获得高频数据。人们可以希望，这里开发的一些统计方法可以在这些领域中找到应用。