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Dive into the research topics where Jérôme Lelong is active.

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Featured researches published by Jérôme Lelong.


Monte Carlo Methods and Applications | 2013

A Parallel Algorithm for solving BSDEs

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

Stochastic Local Intensity Loss Models with Interacting Particle Systems

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

STOCHASTIC LOCAL INTENSITY LOSS MODELS WITH INTERACTING PARTICLE SYSTEMS

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

A CLOSED-FORM EXTENSION TO THE BLACK-COX MODEL

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

Pricing Parisian options using Laplace transforms

Céline Labart; Jérôme Lelong


arXiv: Probability | 2011

A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options

Céline Labart; Jérôme Lelong


arXiv: Probability | 2016

Stochastic modelling of thermal effects on a ferromagnetic nano particle

Stéphane Labbé; Jérôme Lelong


arXiv: Probability | 2016

Pricing American options using martingale bases

Jérôme Lelong


Applied Numerical Mathematics | 2016

Robust adaptive numerical integration of irregular functions with applications to basket and other multi-dimensional exotic options

Christophe De Luigi; Jérôme Lelong; Sylvain Maire


Archive | 2013

New Results - Credit risk

Aurélien Alfonsi; Céline Labart; Jérôme Lelong

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Damien Lamberton

University of Marne-la-Vallée

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Vlad Bally

University of Marne-la-Vallée

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