Geodesic
Numerical approximations of McKean anticipative backward stochastic differential equations arising in initial margin requirements
A. Agarwal1 ; S. De Marco2 ; E. Gobet3 ; J. G. López-Salas4 ; F. Noubiagain5 ; A. Zhou6
1Adam Smith Business School, University of Glasgow, University Avenue, G12 8QQ Glasgow, United Kingdom
2Centre de Mathématiques Appliqués (CMAP), Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France
3CMAP, Ecole Polytechnique
4Department of Mathematics, Faculty of Informatics, Universidade da Coruña, Campus de Elviña s/n, 15071 - A Coruña, Spain
5This author research was conducted while at Laboratoire Manceau de Mathématiques, Le Mans Université, France
6This author research was conducted while at Université Paris-Est, CERMICS (ENPC), 77455, Marne-la-Vallé, France
ESAIM. Proceedings, Tome 65 (2019), pp. 1-26
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We introduce a new class of anticipative backward stochastic differential equations with a dependence of McKean type on the law of the solution, that we name MKABSDE. We provide existence and uniqueness results in a general framework with relatively general regularity assumptions on the coefficients. We show how such stochastic equations arise within the modern paradigm of derivative pricing where a central counterparty (CCP) requires the members to deposit variation and initial margins to cover their exposure. In the case when the initial margin is proportional to the Conditional Value-at-Risk (CVaR) of the contract price, we apply our general result to define the price as a solution of a MKABSDE. We provide several linear and non-linear simpler approximations, which we solve using different numerical (deterministic and Monte-Carlo) methods.
DOI : 10.1051/proc/201965001

A. Agarwal  1   ; S. De Marco  2   ; E. Gobet  3   ; J. G. López-Salas  4   ; F. Noubiagain  5   ; A. Zhou  6

1 Adam Smith Business School, University of Glasgow, University Avenue, G12 8QQ Glasgow, United Kingdom
2 Centre de Mathématiques Appliqués (CMAP), Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France
3 CMAP, Ecole Polytechnique
4 Department of Mathematics, Faculty of Informatics, Universidade da Coruña, Campus de Elviña s/n, 15071 - A Coruña, Spain
5 This author research was conducted while at Laboratoire Manceau de Mathématiques, Le Mans Université, France
6 This author research was conducted while at Université Paris-Est, CERMICS (ENPC), 77455, Marne-la-Vallé, France 
@article{EP_2019_65_a1,
     author = {A. Agarwal and S. De Marco and E. Gobet and J. G. L\'opez-Salas and F. Noubiagain and A. Zhou},
     title = {Numerical approximations of {McKean} anticipative backward stochastic differential equations arising in initial margin requirements},
     journal = {ESAIM. Proceedings},
     pages = {1--26},
     year = {2019},
     volume = {65},
     doi = {10.1051/proc/201965001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201965001/}
}
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A. Agarwal; S. De Marco; E. Gobet; J. G. López-Salas; F. Noubiagain; A. Zhou. Numerical approximations of McKean anticipative backward stochastic differential equations arising in initial margin requirements. ESAIM. Proceedings, Tome 65 (2019), pp. 1-26. doi: 10.1051/proc/201965001

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