Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.01185 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916344361910272 |
|---|---|
| author | Agarwal, A. De Marco, S. Gobet, E. Lopez-Salas, J. G. Noubiagain, F. Zhou, A. |
| author_facet | Agarwal, A. De Marco, S. Gobet, E. Lopez-Salas, J. G. Noubiagain, F. Zhou, A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01185 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 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. Zhou, A. Pricing of Securities Optimization and Control Probability 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. |
| title | Numerical approximations of McKean Anticipative Backward Stochastic Differential Equations arising in Initial Margin requirements |
| topic | Pricing of Securities Optimization and Control Probability |
| url | https://arxiv.org/abs/2408.01185 |