Systematic jump risk

In a factor model for a large panel of N asset prices, a random time S is called a “systematic jump time” if it is not a jump time of any of the factors, but nevertheless is a jump time for a significant number of prices: one might for example think that those S’s are jump times of some hidden or unspecified factors. Our aim is to test whether such systematic jumps exist and, if they do, to estimate a suitably defined “aggregated measure” of their sizes. The setting is the usual high frequency setting with a finite time horizon T and observations of all prices and factors at the times iT/n for i = 0, . . . , n. We suppose that both n and N are large, and the asymptotic results (including feasible estimation of the above aggregated measure) are given when both go to infinity, without imposing restrictions on their relative size. In an empirical application, we document the existence of systematic jumps and further show that the associated risk commands a nontrivial risk premium.