Bilateral Credit Valuation Adjustment and First-to-Default Risk
Summary
The document summarizes ways to relate bilateral valuation adjustments to unilateral CVA and DVA. One explanation frames bilateral counterparty risk through scenarios in which both parties survive, the counterparty defaults first, or the institution defaults first. The contingent CVA and DVA components reflect the order of default and can help reconcile the valuation perspectives of the two parties.
Another answer states the common shorthand that bilateral valuation adjustment combines CVA and DVA, accounting for the credit risk of both the counterparty and the reporting entity. A referenced framework connects first-to-default intensities with asset-side CVA and funding costs under simplifying assumptions. The material is a brief collection of answers and a paper reference, not a complete computational recipe; it does not specify exposure models, recovery assumptions, calibration, or implementation details. Its claims therefore need to be read in the context of the assumptions used by a chosen valuation framework.
Key ideas
- Bilateral credit valuation considers possible default by both the counterparty and the institution.
- The bilateral problem can be divided into mutual survival and either party defaulting first.
- Contingent CVA and DVA describe adjustments associated with the order of default.
- A referenced framework links first-to-default intensities to CVA and funding costs under simplifying assumptions.
- The document does not provide enough detail to implement or calibrate a bilateral adjustment.
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Full text
# CVA DVA and Bilateral adjustment # CVA DVA and Bilateral adjustment I've already computed the CVA\DVA and now I would like to compute the bilateral adjustment. Does anyone know the relationship between the CVA\DVA with the bilateral adjustment? I mean a paper, article or whatever; if it talks about that relationship and how to compute the bilateral adjustment, it will be very useful. ## Answer by Mehness (score 1) https://quant.stackexchange.com/a/31092 Hi there not sure if this is what you mean but the paper below is a bit of a classic in the field. The framework essentially allows for characterisation of the bilateral problem as an asset side CVA and symmetric FVA, both driven by first to default intensities once you realise that the DVA 'benefit' and funding cost essentially have the same 'bank defaults first' probability driving them (under some simplifying assumptions at least). So the FTD nature allows a bilateral treatment. The exposition I find very clear in the paper, the best bit being the intuitive integrals derived via feynman kac after the usual PDE treatment. http://www.defaultrisk.com/pa_crdrv_08.htm Burgard, Christoph, Mats Kjaer, "Partial Differential Equation Representations of Derivatives with Bilateral Counterparty Risk and Funding Costs", Journal of Credit Risk, Vol. 7, No. 3, (Fall 2011), pp. 75–93. OOPS - didn't realise how old the question was, sorry, no doubt completely answer completely irrelevant / superfluous now! ## Answer by JB1 (score 1) https://quant.stackexchange.com/a/45689 If we consider the possibility of defaulting ourselves instead of our counterpart, we would arrive at the following case: This is the price we expect our counterpart to see from his side when evaluating the same operation if he calculates his unilateral CVA. To be able to square prices, the alternative would be to calculate the bilateral CVA considering three scenarios instead of two: mutual survival, counterparty makes default first or we default first. These adjustments are known as contingent CVA and DVA. ## Answer by rrg (score 0) https://quant.stackexchange.com/a/39972 Bilateral Valuation Adjustment (or bilateral credit value adjustment), BVA = CVA + DVA This accounts for default of the counterparty and the company itself. Under IFRS13, model-based fair valuation adjustments must take into account all market risk factors. Therefore, both the market value of the counterparty's credit risk, CVA and the counterpart's own counterparty credit risk, DVA, has to be considered.
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