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Stochastic Local Intensity Loss Models with Interacting Particle Systems

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  • Aur\'elien Alfonsi

    (CERMICS, INRIA Paris-Rocquencourt)

  • C\'eline Labart

    (INRIA Paris-Rocquencourt, LAMA)

  • J\'er\^ome Lelong

    (INRIA Paris-Rocquencourt, LJK)

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    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.

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    File URL: http://arxiv.org/pdf/1302.2009
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1302.2009.

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    Date of creation: Feb 2013
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    Publication status: Published in Mathematical Finance 00, 00 (2013) 1-29
    Handle: RePEc:arx:papers:1302.2009

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    Web page: http://arxiv.org/

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    1. Carol Alexander & Leonardo Nogueira, 2004. "Stochastic Local Volatility," ICMA Centre Discussion Papers in Finance, Henley Business School, Reading University icma-dp2008-02, Henley Business School, Reading University, revised Mar 2008.
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