The Econometrics of Distinguishing Jumps from Volatility

区分跳跃和波动的计量经济学

• 批准号: 0350772
• 负责人: Yacine Ait-Sahalia
• 金额: $ 19.08万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0350772&HistoricalAwards=false
• 关键词: Econometrics; Distinguishing; Jumps; Volatility

ABSTRACTPROPOSAL NO: 0350772INSTITUTION: Princeton UniversityNSF PROGRAM: ECONOMICSPI: Ait-Sahalia, YacineTITLE: The Econometrics of Distinguishing Jumps from VolatilityThis research project will develop methods to estimate the volatility parameter with high frequency data when certain complications arise. Two complications that will be studied situations where the Brownian process is contaminated respectively by jumps and market microstructure noise. The PI will develop maximum likelihood techniques to identify the variance with the same degree of precision as if there were no jumps. The PI will then show that this result continues to hold if Levy jumps processes (which are both infinitely more frequent and infinitely small) other than the standard Poisson jumps contaminate the Brownian noise. In the presence of market microstructure noise, the research will study whether it remains optimal to sample the returns process as often as possible for the purpose of estimating the variance consistently with the basic principle that more data is preferred to less. One result shows that, if noise is present but unaccounted for, the optimal sampling frequency is finite. A second result shows that modeling the noise term explicitly restores the first order statistical effect that sampling as often as possible is optimal. This remains true even if one misspecifies the assumed distribution of the noise term. This robustness result argues in favor of incorporating the noise when estimating continuous time models with high frequencyFinancial data, even if one is unsure about the true distribution of the noise term.Ability to decompose total noise into a Brownian part and a discontinuous jump Is useful in a number of contexts: for instance, in option pricing, the two types of noise have different hedging requirements and possibilities; in portfolio allocation, the demand for assets subject to both types of risk can be optimized further if a decomposition of the total risk into a Brownian and a jump part is available; in risk management, such a decomposition makes it possible over short horizons to manage the Brownian risk using Gaussian tools while assessing VaR and other tail statistics based on the identified jump component. Generally, the ability to disentangle jumps from volatility is the essence of risk management, which should focus on controlling large risks while leaving aside the day-to-day Brownian fluctuations. The results of this research will make it possible to distinguish volatility from jumps with perfect accuracy, thereby helping to improve risk management. Understanding how to control for the presence of market microstructure noise is useful in the same contexts. In addition to graduate training, this research will also lay the foundation for international research collaboration.

摘要提案编号：0350772 机构：普林斯顿大学 NSF 项目：ECONOMICSPI：Ait-Sahalia，Yacine 标题：区分波动性跳跃的计量经济学 该研究项目将开发在出现某些复杂情况时用高频数据估计波动性参数的方法。将研究布朗过程分别受到跳跃和市场微观结构噪声污染的两种复杂情况。 PI 将开发最大似然技术，以与没有跳跃相同的精度来识别方差。然后，PI 将表明，如果标准泊松跳跃之外的 Levy 跳跃过程（无限频繁且无限小）污染了布朗噪声，则该结果继续成立。在存在市场微观结构噪音的情况下，该研究将研究尽可能频繁地对回报过程进行采样是否仍然是最佳的，以便根据数据越多越好的基本原则来估计方差。一项结果表明，如果噪声存在但未考虑在内，则最佳采样频率是有限的。第二个结果表明，对噪声项进行建模显式地恢复了一阶统计效应，即尽可能频繁地采样是最佳的。 即使人们错误地指定了噪声项的假设分布，这一点仍然成立。这一稳健性结果支持在估计高频金融数据的连续时间模型时纳入噪声，即使人们不确定噪声项的真实分布。将总噪声分解为布朗部分和不连续跳跃的能力在许多情况下都很有用：例如，在期权定价中，两种类型的噪声具有不同的对冲要求和可能性；在投资组合配置中，如果可以将总风险分解为布朗部分和跳跃部分，则可以进一步优化承受两类风险的资产需求；在风险管理中，这种分解使得可以在短期内使用高斯工具管理布朗风险，同时根据已识别的跳跃成分评估 VaR 和其他尾部统计数据。一般来说，解脱波动性的跳跃能力是风险管理的本质，风险管理的重点应该是控制大风险，而忽略日常的布朗波动。这项研究的结果将能够非常准确地区分波动性和跳跃性，从而有助于改善风险管理。在相同的情况下，了解如何控制市场微观结构噪音的存在是有用的。 除了研究生培养外，这项研究还将为国际研究合作奠定基础。