Modelling Jump Clustering in the Four Major Foreign Exchange Rates Using High-Frequency Returns and Cross-exciting Jump Processes

The study analyses the self-exciting (clustering) and cross-exciting (contagion) effects in the 13 year long time series of 4 major currency exchange rates, namely: EUR/USD, GBP/USD, USD/CHF and USD/JPY. The analysis is performed by applying the univariate and multivariate Hawkes processes to the time series of jumps identified non-parametrically using power-variation estimators calculated from high-frequency returns (15 minute frequency is used). The study finds strong evidence of a statistically significant self-exciting behavior in all of the analyzed time series of “large jumps”. For the series containing even the “small jumps” the self-exciting tendencies remain significant only for the USD/CHF and USD/JPY rates. The study further finds evidence of a limited cross-exciting behavior, with significant relationships between jumps in USD/JPY and the future jump intensity in USD/CHF, as well as between jumps in USD/CHF and the future jump intensity of EUR/USD.