We present a statistical test that ascertains whether price jumps following an assumed model have a significant influence on pricing options. The rationale behind our approach is that if the jump size and/or frequency is small relative to the volatility of the jump-free base process, then one can use a simpler jump-free simple model. Our test is based on simulating the sensitivity of the option price with respect to an assumed jump model. The sensitivity estimator infers jumps to the base price process at stopping times or observation times.
The presented hypothesis test outperforms the t-test for the difference in means, in terms of the probability of rejecting the null hypothesis, in both settings: when the volatility of the diffusion process is dominant, or when the Poisson jump behavior is dominant.
This is joint research with Svetlana Borovkova and Bernd Heidergott.