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I was wondering why xVA, according to its definition, is applicable only to derivatives contract. For example shouldn't be applicable to corporate loans as well? The counterparty who borrowed the money has a probability of default therefore the risk free value of the loans portfolio is different than the actual one.

I understand that this is linked to the interest rates (i.e ir depends on the credit quality of the counterparty) but isn't it more consistent to calculate a “no-default value” and then reduced it by the expected loss due to the possibility of a default(CVA)?

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  • $\begingroup$ I guess theoretically you could apply "CVA" to loans/bonds. But that wouldn't be as consistent as using credit spread or hazard rate. Different coupons and maturities could make things really messy if you apply CVA to every unique loan/bond $\endgroup$ – Will Gu Apr 1 '18 at 4:56
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You are right, there's not much difference. I think the reason people don't talk about it that way is due to accounting. Derivatives are marked to market (thus requiring an accurate estimate of future credit losses, thus CVA) , whereas loans are typically carried on the books at par value, until they become impaired due to non payment in which case a provision is taken.

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I don’t think it is exactly correct to say that XVA only apply to derivatives. It is more correct to say they are more relevant to derivatives than cash products such as loans. The reason is that in cash products, the expected exposure is always known. If you have a $\$1m$ loan, your exposure is always $\$1m$ and the credit risk will be incorporated in the interest rate you pay on that loan.

On the other hands with derivatives, the exposure in the future is unknown ( it will depends on the levels of interest rates for swaps, of FX rates of FX products etc). It is thus much harder to asses the impact of a default in say one year time as the exposure in one year time is a random variable.

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I don't think that would be possible. First of all, take into account that these adjustments are useful for pricing and risk management (not accounting). So, for debt obligations we already have the traditional Credit Risk approach which "adjust" the price through the spreads. However, for the derivatives transactions (at OTC markets level) there was nothing similar, so these kind of adjustments can be used.

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For a portfolio of loans, the expected loss is considered as a cost and not a risk. Usually, one would compute this expected loss, price it in the loan's interest and set it aside (provision). The risk comes from the unexpected loss, it is computed as a value at risk or expected shortfall.

For a portfolio of bonds, you have issuer risk but not counterparty risk.

For portfolio of derivatives, you can't use the approach above because something as simple as determining the exposure at defaut EAD becomes very complicated and requires Monte Carlo simulation, so the market has come up with the CVA which is a price adjustment to take into account the risk that the counterpart could default, this CVA can charged to the counteparty, (partially) hedged, and it is subject to a capital charge (VaR on CVA).

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