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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.

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3 Answers 3

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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).

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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

  1. 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 $V(t)$

  2. 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 $t$

  1. 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.

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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

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  • $\begingroup$ You never model credit events explicitly for CVA $\endgroup$
    – achirikhin
    Commented May 27 at 22:55
  • $\begingroup$ the spirit of the default probability is to measure credit events... $\endgroup$
    – Yuca
    Commented Jun 2 at 3:27

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