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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.

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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!

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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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If we consider the possibility of defaulting ourselves instead of our counterpart, we would arrive at the following case:

enter image description here

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.

enter image description here

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