Maged
Member
Hi
Could you help in providing quick comparison & relation between them.
Much appreciated
Could you help in providing quick comparison & relation between them.
Much appreciated
Credit VaR vs CVA
- Thread starter Maged
- Start date
Hi @Maged That's a great question, which could lead to deep discussion with respect to practice-oriented differences. I would start with this: the credit value adjustment (CVA), because it assigns a price to counterparty risk, is essentially an estimate of expected (future) losses, while credit value at risk (CVaR) is an estimate of (future) potential unexpected losses (UL). At the risk of brutal and indefensible simplification 
: CVA --> EL and CVaR --> UL. Both refer to credit risk and they do complement (we can calculate CVA and CVaR for the same credit exposure). The CVA adjustment reduces the (mark to market) value of a position by pricing its counterparty risk, while the CVaR would inform the (regulatory or economic) capital buffer in anticipation of the unexpected losses; ie., expected losses are typically "priced into" products or expensed into P&Ls as an income statement perspective, whereas unexpected losses are typical an issue of capital buffer as a balance sheet perspective. Philosophically, I think we could say they both concern the future distribution of a credit exposure where the CVA concerns the precisely-measured mean of the future distribution (note the CVA formula is basically an time-informed EL = PD*EAD*LGD) while CVaR is the approximately-estimated loss quantile (minus the EL). I hope that's a helpful frame!
: CVA --> EL and CVaR --> UL. Both refer to credit risk and they do complement (we can calculate CVA and CVaR for the same credit exposure). The CVA adjustment reduces the (mark to market) value of a position by pricing its counterparty risk, while the CVaR would inform the (regulatory or economic) capital buffer in anticipation of the unexpected losses; ie., expected losses are typically "priced into" products or expensed into P&Ls as an income statement perspective, whereas unexpected losses are typical an issue of capital buffer as a balance sheet perspective. Philosophically, I think we could say they both concern the future distribution of a credit exposure where the CVA concerns the precisely-measured mean of the future distribution (note the CVA formula is basically an time-informed EL = PD*EAD*LGD) while CVaR is the approximately-estimated loss quantile (minus the EL). I hope that's a helpful frame!
Maged
Member
Many thanks @David Harper CFA FRM
Is it right to say that from application point of view:
- Credit VaR is for loans provided to retail & corporate
- CVA is for exposure at counterparty (Opposite side with a financial institution)
I'm looking for practical application on the ground for solid understanding
Is it right to say that from application point of view:
- Credit VaR is for loans provided to retail & corporate
- CVA is for exposure at counterparty (Opposite side with a financial institution)
I'm looking for practical application on the ground for solid understanding
Hi @Maged,
I think you can calculate both the CVA and the CVaR for Corporate/Retail Loans as well as any security based Counterparty exposure. In line with what @David Harper CFA FRM has pointed out, I would hazard that CVA is more of an Accounting Measure that tries to incorporate the Expected Losses in the Statement of P/L (Income Statement). There are currently discussions going on in the Accounting world regarding the validity of using CVA as well as its sister, the DVA (notorious) ( to reduce the amount of recoverable / to increase the amount recoverable from a counterparty ). CVA is like a provision for Bad and Doubtful debts where we can only provide for the known losses, here the expected losses.
CVaR on the other hand is nothing but a cousin of VaR where we find the Worst case loss in excess of Expected Loss which in turn can be used to set the amount of Capital needed to be set aside for the Credit Risks, in other words, we increase or decrease the Amount of Capital by using the CVaR. So, this is an addition to the Capital by using the Profits and by extension, other sources of funds, whereas CVA is a direct reduction from the amount of Exposure by a direct charge to the P/L ( more like an expense, provision)
I would say that the CVaR is like a Reserve for unexpected losses or say a contingent liability in our Balance Sheets.
CVA is the price or value of the expected losses from counterparty defaulting or any other expected counterparty credit risk event for say any period of time whereas the CVaR is only computed for one year or so at a given confidence level. Also note that the same counterparty risk event may have some unexpected or unusual losses which is captured by CVaR
Look at the formula for Credit Risk capital:
LGD*EAD*(WCDR-PD)
As you can see, the formula incorporates the WCDR over and above the PD, we know that LGD*EAD*PD is EL or CVA to be exact, therefore, the Credit Risk Capital and by extension the CVaR is Worst Case Loss over and above the EL or CVA, if you look at the Curve that was presented on many questions on this topic, we can roughly say that
This is @David Harper CFA FRM's own image used in another series of discussion on CVaR. As you can see, the CVA portion would roughly lie where the EL is or the thin area of difference between par value and expected terminal value. The CVaR on the other hand is the area corresponding to the full UL ( Credit VaR+EL) -EL or the Terminal Value of the Bond - Quantile Value
Hope this helps somewhat and David, please do correct me if I am wrong
I think you can calculate both the CVA and the CVaR for Corporate/Retail Loans as well as any security based Counterparty exposure. In line with what @David Harper CFA FRM has pointed out, I would hazard that CVA is more of an Accounting Measure that tries to incorporate the Expected Losses in the Statement of P/L (Income Statement). There are currently discussions going on in the Accounting world regarding the validity of using CVA as well as its sister, the DVA (notorious) ( to reduce the amount of recoverable / to increase the amount recoverable from a counterparty ). CVA is like a provision for Bad and Doubtful debts where we can only provide for the known losses, here the expected losses.
CVaR on the other hand is nothing but a cousin of VaR where we find the Worst case loss in excess of Expected Loss which in turn can be used to set the amount of Capital needed to be set aside for the Credit Risks, in other words, we increase or decrease the Amount of Capital by using the CVaR. So, this is an addition to the Capital by using the Profits and by extension, other sources of funds, whereas CVA is a direct reduction from the amount of Exposure by a direct charge to the P/L ( more like an expense, provision)
I would say that the CVaR is like a Reserve for unexpected losses or say a contingent liability in our Balance Sheets.
CVA is the price or value of the expected losses from counterparty defaulting or any other expected counterparty credit risk event for say any period of time whereas the CVaR is only computed for one year or so at a given confidence level. Also note that the same counterparty risk event may have some unexpected or unusual losses which is captured by CVaR
Look at the formula for Credit Risk capital:
LGD*EAD*(WCDR-PD)
As you can see, the formula incorporates the WCDR over and above the PD, we know that LGD*EAD*PD is EL or CVA to be exact, therefore, the Credit Risk Capital and by extension the CVaR is Worst Case Loss over and above the EL or CVA, if you look at the Curve that was presented on many questions on this topic, we can roughly say that
This is @David Harper CFA FRM's own image used in another series of discussion on CVaR. As you can see, the CVA portion would roughly lie where the EL is or the thin area of difference between par value and expected terminal value. The CVaR on the other hand is the area corresponding to the full UL ( Credit VaR+EL) -EL or the Terminal Value of the Bond - Quantile Value
Hope this helps somewhat and David, please do correct me if I am wrong
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