Numerical approximations of McKean anticipative backward stochastic differential equations arising in initial margin requirements

Agarwal, A. , De Marco, S., Gobet, E., Lopez-Salas, J.-G., Noubiagain, F. and Zhou, A. (2019) Numerical approximations of McKean anticipative backward stochastic differential equations arising in initial margin requirements. ESAIM: Proceedings and Surveys, 65, pp. 1-26. (doi: 10.1051/proc/201965001)

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Abstract

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.

Item Type:Articles
Keywords:Non-linear pricing, CVaR initial margins, anticipative BSDE, weak non-linearity.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Agarwal, Dr Ankush
Authors: Agarwal, A., De Marco, S., Gobet, E., Lopez-Salas, J.-G., Noubiagain, F., and Zhou, A.
Subjects:H Social Sciences > HG Finance
Q Science > QA Mathematics
College/School:College of Social Sciences > Adam Smith Business School > Economics
Journal Name:ESAIM: Proceedings and Surveys
Publisher:EDP Sciences
ISSN:2267-3059
ISSN (Online):2267-3059
Copyright Holders:Copyright © 2019 EDP Sciences, SMAI
First Published:First published in ESAIM: Proceedings and Surveys 65:1-26
Publisher Policy:Reproduced under a Creative Commons License

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