Model-Based Estimation of High Frequency Jump Diffusions with Microstructure Noise and Stochastic Volatility

Abstract

When analysing the volatility related to high frequency financial data, mostly nonparametric approaches based on realised or bipower variation are applied. This article instead starts from a continuous time diffusion model and derives a parametric analog at high frequency for it, allowing simultaneously for microstructure effects, jumps, missing observations and stochastic volatility.Estimation of the model delivers measures of daily variation outperforming their nonparametric counterparts. Both with simulated and actual exchange rate data, the feasibility of this novel approach is shown. The parametric setting is used to estimate the intra-day trend in the Euro/U.S. Dollar exchange rate.

Robust estimation of intraweek periodicity in volatility and jump detection

“…Periodicity estimates have been used for disentangling the periodic variation in volatility and the impact of news on intraday volatility (Andersen et al, 2003;Dominguez and Panthaki, 2006), forecasting of intraday variance (Martens et al, 2002) and efficient estimation of daily volatility using high-frequency returns (Areal and Taylor, 2002;Bos, 2008). For all these applications, it is natural to use a jump-robust periodicity estimate.…”

“…If there are jumps, more observations are downweighted. The WSD in (2.12) has a 69% efficiency under normality of the r i s, as opposed to the 37% efficiency of the ShortH (see Boudt et al, 2008, for details).…”

Spot Variance Path Estimation and Its Application to High-Frequency Jump Testing

“…Moreover, realized jumps can provide an insight into the nature of jumps for asset classes or common movements (co-jumps) between assets, see Lahaye, Laurent, and Neely (2009). Parametric methods to test for jumps are adapted by Duan and Fülöp (2007) and Bos (2008) where jumps are detected as part of the estimation method. Boudt et al (2008) have shown that pronounced intraday periodicity leads to the distorted jump inference based on the Lee and Mykland (2008) test.…”

Robust Estimation of Intraweek Periodicity in Volatility and Jump Detection

“…Andersen and Bollerslev (1997b) and Andersen et al (2007a) document the importance of allowing for jumps and for periodicity of intraday volatility in the nonparametric estimation and forecasting of volatility, but treat these two features separately. Periodicity estimates that are robust to price jumps are needed for disentangling the periodic variation in volatility and the impact of news on intraday volatility (Dominguez and Panthaki, 2006), forecasting of intraday variance (Martens et al, 2002), efficient estimation of daily volatility using high-frequency returns (Areal and Taylor, 2002;Bos, 2008) and, as we show in this paper, for intraday jump detection.…”