Estimating bivariate GARCH-Jump Model Based on High Frequency Data: the Case of Revaluation of the Chinese Yuan in July 2005

This paper attempts to model the behavior of 1-minute high frequency exchange rate data of 5 currencies : the Japanese Yen, the Australian Dollar, the Canadian Dollar, the Euro, the Pound sterling against the US Dollar, on 21 July 2005 when the Chinese Yuan was revaluated. The data shows the following distinctive features: (1) There is a large jump at the time of the Yuan revaluation, (2) Large volatility is observed for a while after the jump, (3) There were many other jumps, possibly correlated, in each exchange rate time series. To capture these features we fit the following models to the data: (i) One dimensional GARCH-Jump model with a large jump which is influential on volatility, and (ii) a bivariate GARCH-Jump model with correlated Poisson jumps. For comparison, we also esimate one and two dimensional GARCH model without jumps. The model performance is evaluated based on Value-at-Risk (VaR).