Simulation-Based Exact Tests with Unidentified Nuisance Parameters Under the Null Hypothesis: the Case of Jumps Tests in Models with Conditional Heteroskedasticity

We use the Monte-Carlo (MC) test technique to find valid p-values when testing for discontinuities in jump-diffusion models. While the distribution of the LR statistic for this test is typically non-standard, we show that the MC p-value is finite sample exact if no other (identified) nuisance parameter is present. Otherwise, we derive nuisance-parameter free bounds and obtain exact bounds p-values. We illustrate our approach on four classes of jump-diffusion models we use to models spot prices of copper, nickel, golds, and crude oil. We find significant jumps in all weekly time series and in a few monthly time series.