The Econometrics of Distinguishing Jumps from Volatility

Princeton University, Princeton NJ

Investigators

Abstract

ABSTRACT PROPOSAL NO: 0350772 INSTITUTION: Princeton University NSF PROGRAM: ECONOMICS PI: Ait-Sahalia, Yacine TITLE: The Econometrics of Distinguishing Jumps from Volatility This 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 frequency Financial 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.