Sensitivity Analysis for Marked Hawkes Processes - Application to CLO Pricing

Abstract

This paper introduces a model for pricing Collateralized Loan Obligations, where the underlying credit risk is driven by a marked Hawkes process, involving both clustering effects on defaults and random recovery rates. We provide a sensitivity analysis of the CLO price with respect to the parameters of the Hawkes process using a change of probability and a variational approach. We also provide a simplified version of the model where the intensity of the Hawkes process is taken as the instantaneous default rate. In this setting, we give a moment-based formula for the expected survival probability.

Keywords: Change of Probability, Credit Derivatives, Poisson Processes, Hawkes Processes, Sensitivity Analysis