Céline Labart

Simulation of BSDEs by Wiener chaos expansion

We present an algorithm to solve BSDEs based on Wiener Chaos Expansion and Picards iterations. We get a forward scheme where the conditional expectations are easily computed thanks to chaos decomposition formulas. We use the Malliavin derivative to compute

A Parallel Algorithm for solving BSDEs

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Stochastic Local Intensity Loss Models with Interacting Particle Systems

. Concerning the error, we derive explicit bounds with respect to the number of chaos and the discretization time step. We also present numerical experiments. We obtain very encouraging results in terms of speed and accuracy.

STOCHASTIC LOCAL INTENSITY LOSS MODELS WITH INTERACTING PARTICLE SYSTEMS

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.

Simulation of BSDEs with jumps by Wiener Chaos Expansion

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.

Pricing Parisian options using Laplace transforms

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.