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Counterparty Credit Exposures for Interest Rate Derivatives using the Stochastic Grid Bundling Method

Karlsson, Patrik LU ; Jain, Shashi and Oosterlee, Cornelis W. (2016) In Applied Mathematical Finance p.175-196
Abstract

The regulatory credit value adjustment (CVA) for an outstanding over-the-counter (OTC) derivative portfolio is computed based on the portfolio exposure over its lifetime. Usually, the future portfolio exposure is approximated using the Monte Carlo simulation, as the portfolio value can be driven by several market risk-factors. For derivatives, such as Bermudan swaptions, that do not have an analytical approximation for their Mark-to-Market (MtM) value, the standard market practice is to use the regression functions from the least squares Monte Carlo method to approximate their MtM along simulated scenarios. However, such approximations have significant bias and noise, resulting in inaccurate CVA charge. In this paper, we extend the... (More)

The regulatory credit value adjustment (CVA) for an outstanding over-the-counter (OTC) derivative portfolio is computed based on the portfolio exposure over its lifetime. Usually, the future portfolio exposure is approximated using the Monte Carlo simulation, as the portfolio value can be driven by several market risk-factors. For derivatives, such as Bermudan swaptions, that do not have an analytical approximation for their Mark-to-Market (MtM) value, the standard market practice is to use the regression functions from the least squares Monte Carlo method to approximate their MtM along simulated scenarios. However, such approximations have significant bias and noise, resulting in inaccurate CVA charge. In this paper, we extend the Stochastic Grid Bundling Method (SGBM) for the one-factor Gaussian short rate model, to efficiently and accurately compute Expected Exposure, Potential Future exposure and CVA for Bermudan swaptions. A novel contribution of the paper is that it demonstrates how different measures, for instance spot and terminal measure, can simultaneously be employed in the SGBM framework, to significantly reduce the variance and bias of the solution.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Bermudan Swaptions, credit value adjustment (CVA), Monte Carlo Simulation, stochastic grid bundling method (SGBM), XVA
in
Applied Mathematical Finance
pages
22 pages
publisher
Routledge
external identifiers
  • scopus:84984865038
ISSN
1350-486X
DOI
10.1080/1350486X.2016.1226144
language
English
LU publication?
yes
id
5540ab20-162c-4ab5-9c23-d27a02df745a
date added to LUP
2016-10-19 21:06:22
date last changed
2017-01-01 08:37:15
@article{5540ab20-162c-4ab5-9c23-d27a02df745a,
  abstract     = {<p>The regulatory credit value adjustment (CVA) for an outstanding over-the-counter (OTC) derivative portfolio is computed based on the portfolio exposure over its lifetime. Usually, the future portfolio exposure is approximated using the Monte Carlo simulation, as the portfolio value can be driven by several market risk-factors. For derivatives, such as Bermudan swaptions, that do not have an analytical approximation for their Mark-to-Market (MtM) value, the standard market practice is to use the regression functions from the least squares Monte Carlo method to approximate their MtM along simulated scenarios. However, such approximations have significant bias and noise, resulting in inaccurate CVA charge. In this paper, we extend the Stochastic Grid Bundling Method (SGBM) for the one-factor Gaussian short rate model, to efficiently and accurately compute Expected Exposure, Potential Future exposure and CVA for Bermudan swaptions. A novel contribution of the paper is that it demonstrates how different measures, for instance spot and terminal measure, can simultaneously be employed in the SGBM framework, to significantly reduce the variance and bias of the solution.</p>},
  author       = {Karlsson, Patrik and Jain, Shashi and Oosterlee, Cornelis W.},
  issn         = {1350-486X},
  keyword      = {Bermudan Swaptions,credit value adjustment (CVA),Monte Carlo Simulation,stochastic grid bundling method (SGBM),XVA},
  language     = {eng},
  month        = {10},
  pages        = {175--196},
  publisher    = {Routledge},
  series       = {Applied Mathematical Finance},
  title        = {Counterparty Credit Exposures for Interest Rate Derivatives using the Stochastic Grid Bundling Method},
  url          = {http://dx.doi.org/10.1080/1350486X.2016.1226144},
  year         = {2016},
}