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.

该研究项目开发了以高频采样的连续时间半明星模型的新估计和推理工具。 Semimartingale模型是排除套利机会的资产价格最通用的模型，结果是现代资产定价中的主力模型。拟议活动的主要知识分子是开发了新的非线性回归方法，该方法具有潜在的潜在方式半明星作为回归剂的波动过程。挥发性过程测量了半木制的内在变异性。这些方法将使研究人员能够研究经济变量与波动率过程之间的统计关系，而无需实现强烈的假设。拟议活动可以分为三个部分。第一部分涉及涉及波动率的基线矢量非线性回归模型。估计分两个步骤进行。在第一步中，潜在的波动过程以无模型方式从高频数据中恢复，在第二步中，通过通用矩（GMM）估算回归模型。研究了此过程的统计属性。这些工具允许用户探索波动性过程如何驱动其他经济变量并制作统计正式陈述。包括经验应用程序以说明方法的使用。第二部分通过允许记录模型可能被误指定来扩展第一部分。该扩展在现实环境中阐明了估计方法的鲁棒性，在现实设置中，回归模型仅被视为真实模型的近似值。对错误指定模型的分析促进了竞争模型的比较和评估。第三部分引入了一个新的回归框架，该框架可用于对潜在波动率过程的样本路径进行非线性投影，以在另一个波动性过程的过程中。在财务应用中，该方法可用于探索多个资产的波动如何彼此共同。拟议活动中的激励示例是财务模型的示例，但该项目中开发的方法对于通用半明星有效。除了经济学和金融外，半明星还用于高频数据的生物，化学和电气应用中。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程序。