High-frequency financial data modeling using Hawkes processes
Intraday Value-at-Risk (VaR) is one of the risk measures used by market participants involved in high-frequency trading. High-frequency log-returns feature important kurtosis (fat tails) and volatility clustering (extreme log-returns appear in clusters) that VaR models should take into account. We propose a marked point process model for the excesses of the time series over a high threshold that combines Hawkes processes for the exceedances with a generalized Pareto distribution model for the marks (exceedance sizes). The conditional approach features intraday clustering of extremes and is used to calculate instantaneous conditional VaR. The models are backtested on real data and compared to a competitor approach that proposes a nonparametric extension of the classical peaks-over-threshold method. Maximum likelihood estimation is computationally intensive; we use a differential evolution genetic algorithm to find adequate starting values for the optimization process.
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- Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
- McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
- Dionne, Georges & Duchesne, Pierre & Pacurar, Maria, 2009.
"Intraday Value at Risk (IVaR) using tick-by-tick data with application to the Toronto Stock Exchange,"
Journal of Empirical Finance,
Elsevier, vol. 16(5), pages 777-792, December.
- Georges Dionne & Pierre Duchesne & Maria Pacurar, 2005. "Intraday Value at Risk (IVaR) Using Tick-by-Tick Data with Application to the Toronto Stock Exchange," Cahiers de recherche 0533, CIRPEE.
- Pierre Giot, 2005. "Market risk models for intraday data," The European Journal of Finance, Taylor & Francis Journals, vol. 11(4), pages 309-324.
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