Jérôme Lelong
Joseph Fourier University
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Publication
Featured researches published by Jérôme Lelong.
Monte Carlo Methods and Applications | 2013
Céline Labart; Jérôme Lelong
Abstract. We present a parallel algorithm for solving backward stochastic differential equations. We improve the algorithm proposed by Gobet and Labart (2010) based on an adaptive Monte Carlo method with Picards iterations, and propose a parallel version of it. We test our algorithm on linear and nonlinear drivers up to dimension 8 on a cluster of 312 CPUs. We obtained very encouraging efficiency ratios greater than 0.7.
arXiv: Probability | 2016
Aurélien Alfonsi; Céline Labart; Jérôme Lelong
It is well-known from the work of Schonbucher (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.
Mathematical Finance | 2016
Aurélien Alfonsi; Céline Labart; Jérôme Lelong
It is well-known from the work of Schonbucher (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.
International Journal of Theoretical and Applied Finance | 2012
Aurélien Alfonsi; Jérôme Lelong
In the Black-Cox model, a firm defaults when its value hits an exponential barrier. Here, we propose an hybrid model that generalizes this framework. The default intensity can take two different values and switches when the firm value crosses a barrier. Of course, the intensity level is higher below the barrier. We get an analytic formula for the Laplace transform of the default time. This result can be also extended to multiple barriers and intensity levels. Then, we explain how this model can be calibrated to Credit Default Swap prices and show its tractability on different kinds of data. We also present numerical methods to numerically recover the default time distribution.
Bankers Markets & Investors : an academic & professional review | 2009
Céline Labart; Jérôme Lelong
arXiv: Probability | 2011
Céline Labart; Jérôme Lelong
arXiv: Probability | 2016
Stéphane Labbé; Jérôme Lelong
arXiv: Probability | 2016
Jérôme Lelong
Applied Numerical Mathematics | 2016
Christophe De Luigi; Jérôme Lelong; Sylvain Maire
Archive | 2013
Aurélien Alfonsi; Céline Labart; Jérôme Lelong