STOCHASTIC LOCAL INTENSITY LOSS MODELS WITH INTERACTING PARTICLE SYSTEMS

Authors


  • We would like to thank Benjamin Jourdain (Université Paris-Est) for fruitful discussions having stimulated this research. We would like to thank INRIA Paris Rocquencourt for allowing us to run our numerical tests on the convergence rate on their RIOC cluster. A. Alfonsi acknowledges the support of the “Chaire Risques Financiers” of Fondation du Risque. This project partly benefited from the support of the Finance for Energy Market Research Centre, www.fime-lab.org.

Abstract

It is well known from the work of Schönbucher 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 allow to get a stochastic jump intensity while keeping the same marginal laws. These models involve a nonlinear stochastic differential equation (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 toward the nonlinear 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.

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