Stochastic Local Intensity Loss Models with Interacting Particle Systems

TL;DR

This paper proves the existence and uniqueness of Stochastic Local Intensity models using interacting particle systems and demonstrates efficient computation of pathwise expectations with these models.

Contribution

It introduces a novel proof of existence and uniqueness for SLI models via interacting particle systems and analyzes their convergence and computational efficiency.

Findings

Proved existence and uniqueness of SLI models.

Analyzed convergence rate of particle systems.

Demonstrated efficient computation of expectations.

Abstract

It is well-known from the work of Sch\"onbucher (2005) that the marginal laws of a loss process can be matched by a unit increasing time inhomogeneous Markov process, whose deterministic jump intensity is called local intensity. The Stochastic Local Intensity (SLI) models such as the one proposed by Arnsdorf and Halperin (2008) allow to get a stochastic jump intensity while keeping the same marginal laws. These models involve a non-linear SDE with jumps. The first contribution of this paper is to prove the existence and uniqueness of such processes. This is made by means of an interacting particle system, whose convergence rate towards the non-linear SDE is analyzed. Second, this approach provides a powerful way to compute pathwise expectations with the SLI model: we show that the computational cost is roughly the same as a crude Monte-Carlo algorithm for standard SDEs.