Testing for jumps and cojumps in financial markets

[摘要] In this thesis, we introduce a new testing methodology to detect cojumps in multi-asset returns. We define a cojump as a jump in at least one dimension of the return processes. For a multivariate process that follows a semimartingale, and with no other specific assumptions on the process, we form a test statistic which can easily disentangle jumps from continuous paths of the process. We prove that the test statistics are chi-square distributed in the absence of jumps in any dimensions. We propose a hypothesis testing based on the extreme distribution of the test statistics. If the test statistic observed is beyond the extreme level, then most likely, a cojump occurs. Monte Carlo simulation is performed to access the effectiveness of the test by examining the size and power of the test. We apply the test to a pair of empirical asset returns data and the findings of jump timing are consistent with existing literature.

[发布机构] Massachusetts Institute of Technology