Doubly reflected BSDEs with call protection and their approximation

Jean-François Chassagneux; Stéphane Crépey

ESAIM: Probability and Statistics (2014)

  • Volume: 18, page 613-641
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Chassagneux, Jean-François, and Crépey, Stéphane. "Doubly reflected BSDEs with call protection and their approximation." ESAIM: Probability and Statistics 18 (2014): 613-641. <http://eudml.org/doc/274342>.

@article{Chassagneux2014,
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.},
author = {Chassagneux, Jean-François, Crépey, Stéphane},
journal = {ESAIM: Probability and Statistics},
keywords = {reflected BSDEs; variational inequalities; discrete-time approximation; game option; Call protection; reflected backward stochastic differential equations (BSDEs); call protection},
language = {eng},
pages = {613-641},
publisher = {EDP-Sciences},
title = {Doubly reflected BSDEs with call protection and their approximation},
url = {http://eudml.org/doc/274342},
volume = {18},
year = {2014},
}

TY - JOUR
AU - Chassagneux, Jean-François
AU - Crépey, Stéphane
TI - Doubly reflected BSDEs with call protection and their approximation
JO - ESAIM: Probability and Statistics
PY - 2014
PB - EDP-Sciences
VL - 18
SP - 613
EP - 641
AB - 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.
LA - eng
KW - reflected BSDEs; variational inequalities; discrete-time approximation; game option; Call protection; reflected backward stochastic differential equations (BSDEs); call protection
UR - http://eudml.org/doc/274342
ER -

References

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