Skip to content
All library documents

A Monte Carlo Workflow for Credit Valuation Adjustment

Article Quant Q&A · Author: Amit
Read the original

Summary

The document collects pointers on computational approaches to Credit Valuation Adjustment (CVA), including a brief simulation workflow for counterparty exposure. Under an independence assumption between counterparty credit and the market factors driving portfolio value, simulate risk-neutral paths for those factors, reprice the portfolio at future times, and estimate expected positive exposure at each time. Discounted expected exposure is then integrated against the counterparty’s default probability, with loss severity determined by one minus recovery.

The answers identify time stepping, market simulation, portfolio repricing, and default probability modeling as computational concerns. The workflow is a simplified setup: it assumes independence between credit and market drivers and does not detail calibration, numerical convergence, collateral, netting, or wrong-way risk. The source ends during a further answer about credit modeling, so it provides no complete treatment of those topics or a worked numerical experiment.

Key ideas

  • Simulate risk-neutral market factor paths and revalue the portfolio at future time points.
  • Estimate expected exposure using the positive part of portfolio value at each simulated time.
  • Combine discounted expected exposure with the counterparty default probability and loss given default.
  • The stated workflow assumes credit risk is independent of the factors driving portfolio value.
  • Credit modeling and broader portfolio computation challenges are mentioned but not fully developed.

Tags

Fixed incomeRisk managementStatisticsBacktesting
Full text
# Credit Valuation Adjustment Implementation


# Credit Valuation Adjustment Implementation












I am trying to help a friend with her thesis on Counterparty Credit Risk where she intends to have a somewhat lengthy treatment on Credit Valuation Adjustment (CVA). Specifically I am looking to help her in including some computer simulated experiments which would hopefully illustrate CVA calculations under simulated scenarios.

I have been reading a bit on CVA and have got somewhat fair idea of what's going on. However, I am at a loss to find a document where the "Math" has been distilled and computational aspects highlighted, preferably from a programmer's point of view. I have come across a document, which is part of MATLAB's financial toolbox and it does give me some ideas.

I am looking for suggestions/pointers regarding the same.

PS: I am not averse to understanding the Math, just quite perplexed about the "only Math" aspect.

## Answer by rrg (score 1)

https://quant.stackexchange.com/a/39975

There are good examples and spreadsheet solutions in John Gregory (2015). The maths is not complex. Computational aspects are step increments in time and simulation. Math will indicate computation ... ! A matter that requires more imagination is computational simulation on a portfolio basis (see Credit Valuation Adjustments -- computation issues).

## Answer by achirikhin (score 1)

https://quant.stackexchange.com/a/79523

If you can assume that credit is independent of any other factors that drive the future MTM of the reference portfolio (which can be a single trade only), all you need to do is

- generate paths of market factors, driving MTM of the portfolio, under the risk-neutral measure, and reprice the portfolio at each future point on each path; denote the sample vector of such values at time $t$ as $V(t)$

- compute expected exposure of your portfolio at each future time

$EE(t)=E(max(0, V(t)))$,

where V(t) is the value of the portfolio at time $t$

- Plug the $EE(t)$ curve into a CDS loss leg instead of the otherwise constant notional.

$CVA = (1-R)\int^T D(s)EE(s)dP(s)$,

where $D(s)$ is discount factor and $P(s)$ is default probability curve of the counterparty.

## Answer by Yuca (score 0)

https://quant.stackexchange.com/a/45186

The hard part of the CVA computation stems from the default probabilities. There is a lot of literature on how to model credit events, but what was being used at global banks was in the ballpark of what was implemented by Duffie

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.