Multi-Scale Jump and Volatility Analysis for High-Frequency Financial Data

36 Pages Posted: 16 Jan 2007

See all articles by Jianqing Fan

Jianqing Fan

Princeton University - Bendheim Center for Finance

Yazhen Wang

University of Wisconsin - Madison - Department of Statistics; National Science Foundation

Date Written: November 15, 2006

Abstract

The wide availability of high-frequency data for many financial instruments stimulates a upsurge interest in statistical research on the estimation of volatility. Jump-diffusion processes observed with market microstructure noise are frequently used to model high-frequency financial data. Yet, existing methods are developed for either noisy data from a continuous diffusion price model or data from a jump-diffusion price model without noise. We propose methods to cope with both jumps in the price and market microstructure noise in the observed data. They allow us to estimate both integrated volatility and jump variation from the data sampled from jump-diffusion price processes, contaminated with the market microstructure noise. Our approach is to first remove jumps from the data and then apply a noise-resistent method to estimated the integrated volatility. The asymptotic analysis and the simulation study reveal that the proposed wavelet methods can successfully remove the jumps in the price processes and the integrated volatility can be estimated as well as the case with no presence of jumps in the price processes. In addition, they have outstanding statistical efficiency. The methods are illustrated by applications to two high-frequency exchange rate data sets.

Keywords: High-frequency data, integrated volality, microstructure noise, quadratic variation, jump-diffusion, wavelets

JEL Classification: G10, C14

Suggested Citation

Fan, Jianqing and Wang, Yazhen, Multi-Scale Jump and Volatility Analysis for High-Frequency Financial Data (November 15, 2006). Available at SSRN: https://ssrn.com/abstract=957607 or http://dx.doi.org/10.2139/ssrn.957607

Jianqing Fan (Contact Author)

Princeton University - Bendheim Center for Finance ( email )

26 Prospect Avenue
Princeton, NJ 08540
United States
609-258-7924 (Phone)
609-258-8551 (Fax)

HOME PAGE: http://orfe.princeton.edu/~jqfan/

Yazhen Wang

University of Wisconsin - Madison - Department of Statistics ( email )

716 Langdon Street
Madison, WI 53706-1481
United States

National Science Foundation

4201 Wilson Boulevard
Arlington, VA 22230
United States

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