A non-linear PDE for XVA by forward Monte Carlo
Vladimir Piterbarg considers a non-linear partial differentiation equation that appears in a number of XVA-related contexts, including a one-way credit-support annex, credit value adjustment with risky closeout, option pricing with differential borrowing and lending rates, accounting-consistent valuation and constrained cash supply. In showing its solution is given as the minimum of solutions of certain related but linear PDEs, he develops an efficient forward simulation algorithm for any number of dimensions
In this article, a solution to a semi-linear PDE is obtained by taking the minimum of solutions to related linear PDEs over an infinite-dimensional space of discount boundaries. By restricting the minimum to a parameterised subset of boundaries, a practical algorithm for numerically solving the semi-linear PDE in a forward Monte Carlo is obtained. We also show how to modify the standard CVA algorithms to account for the risky closeout in the section on comparison to riskless closeout DVA
Only users who have a paid subscription or are part of a corporate subscription are able to print or copy content.
To access these options, along with all other subscription benefits, please contact info@risk.net or view our subscription options here: http://subscriptions.risk.net/subscribe
You are currently unable to print this content. Please contact info@risk.net to find out more.
You are currently unable to copy this content. Please contact info@risk.net to find out more.
Copyright Infopro Digital Limited. All rights reserved.
You may share this content using our article tools. Printing this content is for the sole use of the Authorised User (named subscriber), as outlined in our terms and conditions - https://www.infopro-insight.com/terms-conditions/insight-subscriptions/
If you would like to purchase additional rights please email info@risk.net
Copyright Infopro Digital Limited. All rights reserved.
You may share this content using our article tools. Copying this content is for the sole use of the Authorised User (named subscriber), as outlined in our terms and conditions - https://www.infopro-insight.com/terms-conditions/insight-subscriptions/
If you would like to purchase additional rights please email info@risk.net
More on Credit markets
Liquidnet sees electronic future for grey bond trading
TP Icap’s grey market bond trading unit has more than doubled transactions in the first quarter of 2024
Single-name CDS trading bounces back
Volumes are up as Covid-driven support fuels opportunity for traders and investors
Podcast: Richard Martin on improving credit migration models
Star quant proposes a new model for predicting changes in bond ratings
CME to pass on Ice CDS administration charges
Clearing house to hike CDS index trade fees from July after Ice’s determinations committee takeover
Buy side fuels boom in single-name CDS clearing
Ice single-name CDS volumes double year on year following switch to semi-annual rolls
Ice to clear single-name bank CDSs from April 10
US participants will be able to start clearing CDSs referencing Ice clearing members
iHeart CDS saga sparks debate over credit rules
Trigger decision highlights product's weaknesses, warns Milbank’s Williams
TLAC-driven CDS index change tipped for September
UK and Swiss bank Holdco CDSs likely inclusions in next iTraxx index roll, say strategists
