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Doubly reflected BSDEs with call protection and their approximation

Published online by Cambridge University Press:  15 October 2014

Jean-François Chassagneux  and
Stéphane Crépey
Jean-François Chassagneux
Affiliation:
Department of Mathematics, Imperial College London, SW7A2Z, London, UK. j.chassagneux@imperial.ac.uk
Stéphane Crépey
Affiliation:
L.A.P. Université d’Evry Val d’Essonne, 91037 Evry, France; stephane.crepey@univ-evry.fr
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Abstract

We study the numerical approximation of doubly reflected backward stochastic differential equations with intermittent upper barrier (RIBSDEs). These denote reflected BSDEs in which the upper barrier is only active on certain random time intervals. From the point of view of financial interpretation, RIBSDEs arise as pricing equations of game options with constrained callability. In a Markovian set-up we prove a convergence rate for a time-discretization scheme by simulation to an RIBSDE. We also characterize the solution of an RIBSDE as the largest viscosity subsolution of a related system of variational inequalities, and we establish the convergence of a deterministic numerical scheme for that problem. Due to the potentially very high dimension of the system of variational inequalities, this approach is not always practical. We thus subsequently prove a convergence rate for a time-discretisation scheme by simulation to an RIBSDE.

Keywords

Reflected BSDEsVariational inequalitiesDiscrete-time approximationGame optionCall protection
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 18 , 2014 , pp. 613 - 641
Copyright
© EDP Sciences, SMAI, 2014

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