Stochastic Local Intensity Loss Models with Interacting Particle Systems

Aurélien Alfonsi (), Céline Labart () and Jérôme Lelong ()
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Aurélien Alfonsi: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées
Céline Labart: LAMA - Laboratoire de Mathématiques - USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc - CNRS - Centre National de la Recherche Scientifique
Jérôme Lelong: DAO - Données, Apprentissage et Optimisation - LJK - Laboratoire Jean Kuntzmann - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA [2016-2019] - Université Grenoble Alpes [2016-2019]

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Abstract: It is well-known from the work of Schönbucher (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.

Keywords: Interacting particle systems; Loss modelling; Stochastic local intensity model; Credit derivatives; Monte-Carlo Algorithm; Martingale problem; Fokker-Planck equation (search for similar items in EconPapers)
Date: 2016-04
Note: View the original document on HAL open archive server: https://hal.science/hal-00786239v1
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Published in Mathematical Finance, 2016, 26 (2), pp.366-394. ⟨10.1111/mafi.12059⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00786239

DOI: 10.1111/mafi.12059

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