Risk that an observed cluster of price jumps has not yet exhausted: performance of an estimate on simulated data

This software is designed to support the research reported in Warnings about future jumps: properties of the Exponential Hawkes model, by Rachele Foschi, Francesca Lilla, and Cecilia Mancini, where it is assumed that the log-prices of a financial asset evolve following a jump diffusion semimartingale, as in (21) within the paper, and the process N counting the jumps is an Exponential Hawkes model. Formula (7) quantifies the probability that an observed cluster of price jumps is not yet finished, while feasible approximations are given by formulas (5) and (6). The software allows to verify, on simulated discrete time data, the reliability of the results obtained with the practical implementation of (5) and (6). The analysis is mentioned in Appendix B.3.4 and produces the results shown in Table 8.