Monte Carlo Algorithms for Default Timing Problems

Abstract

D ynamic, intensity-based point process models are widely used to measure and price the correlated default risk in portfolios of credit-sensitive assets such as loans and corporate bonds. Monte Carlo simulation is an important tool for performing computations in these models. This paper develops, analyzes, and evaluates two simulation algorithms for intensity-based point process models. The algorithms extend the conventional thinning scheme to the case where the event intensity is unbounded, a feature common to many standard model formulations. Numerical results illustrate the performance of the algorithms for a familiar top-down model and a novel bottom-up model of correlated default risk.

A Generalized Contagion Process With an Application to Credit Risk

“…Our model is also the generalisation of so-called generalised Hawkes process used inZhang et al (2009) (see alsoGiesecke and Kim (2007),Giesecke et al (2011) andZhu (2014)) by adding another series of externallyexcited jumps in the underlying intensity process.…”