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Doubly reflected BSDEs with call protection and theirapproximation

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 differentialequations with intermittent upper barrier (RIBSDEs). These denote reflected BSDEs in whichthe upper barrier is only active on certain random time intervals. From the point of viewof financial interpretation, RIBSDEs arise as pricing equations of game options withconstrained callability. In a Markovian set-up we prove a convergence rate for atime-discretization scheme by simulation to an RIBSDE. We also characterize the solutionof an RIBSDE as the largest viscosity subsolution of a related system of variationalinequalities, and we establish the convergence of a deterministic numerical scheme forthat problem. Due to the potentially very high dimension of the system of variationalinequalities, this approach is not always practical. We thus subsequently prove aconvergence 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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