Doubly reflected BSDEs with call protection and their approximation

¹ Department of Mathematics, Imperial College London, SW7A2Z, London, UK
j.chassagneux@imperial.ac.uk
² L.A.P. Université d’Evry Val d’Essonne, 91037 Evry, France
stephane.crepey@univ-evry.fr

Received: 10 April 2012
Revised: 24 January 2013

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.