Calibration of exponential Hawkes processes using a Modified Bionomic Algorithm

The aim of this research is to develop a fast and robust variant of the evolutionary heuristic Bionomic algorithm and assess its contribution to solving complex parametric estimation problems, in conjunction with other traditional optimization techniques. We introduce a modified version of the Bionomic Algorithm (MB), designed to efficiently compute the MLE of self-exciting exponential Hawkes processes with increasing dimensionality of the solution space. Performance tests, performed on simulated and historical S&P 500 financial data, show that the MB algorithm, with its solutions locally improved by either the standard Nelder Mead (NM) or Expectation Maximization (EM) algorithm, converges significantly faster and more frequently to a near-global solution than the NM or EM algorithms operating alone. These test results illustrate the robustness and computational efficiency of the MB algorithm, combined with traditional optimization methods, in the optimization of complex objective functions of high dimensionality.