Credit Valuation Adjustment

Alan — Thu, 12 Nov 2009 15:33:46 GMT

Current revision posted to Credit Risk by Alan on 12/11/2009 15:33:46

Credit Valuation Adjustment

Filed under: Credit Value Adjustment, CVA

Credit value adjustment (CVA) is by definition the difference between the risk-free portfolio value and the true portfolio value that takes into account the possibility of a counterparty’s default. In other words, CVA is the market value of counterparty credit risk.

Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation
can be written as

where T is the maturity of the longest transaction in the portfolio, B(t) is the future value of one unit of the base currency invested today at the prevailing interest rate for maturity t ,1{.} is the indicator function that takes value one if the argument is true (and zero otherwise) and PD(s,t) is the risk neutral probability of counterparty default between times s and t. These probabilities can be obtained from the term structure of credit-default swap
(CDS) spreads.

Exposure, Independent of Counterparty Default

Assuming independence between exposure and counterparty’s credit quality greatly simplifies the analysis. Under this assumption this simplifies to

where

which is the risk-neutral discounted expected exposure (EE)

The Function of the CVA Desk and Implications for Technology Solution

In the view of leading investment banks, CVA is essentially an activity carried out by a trading desk in the Front Office. Tier 1 banks either already generate counterparty EPE and ENE under the ownership of the CVA desk (although this often has another name) or plan to do so. Whilst a CVA platform is based on an exposure measurement platform, the solution drivers are very different and it is unwise to create dependencies between the Risk exposure management system and Front Office CVA system, even if they share similar intermediate outputs.

CVA Operating Model

The originating desks for the OTC trades essentially buy their credit protection from the CVA desk. The credit risk of these desks is thus consolidated into a single book, with the net risk of that book hedged by the CVA desk with the rest of the market.

- The key considerations for a Front Office CVA desk are:

Charge Model
Hedging Portfolio CVA
Proxy Hedging
Hedge Effectiveness
P&L Attribution/Revaluation of Portfolio

References

1. A Guide to Modeling Counterparty Credit Risk, GARP Risk Review, July/August 200, Steven H. Zhu, Michael Pykhtin.

2. EM RISK, Risk Analytics (Credit Value Valuation Adjustment Solution Consultants)

Credit Valuation Adjustment

Alan — Thu, 12 Nov 2009 15:33:19 GMT

Revision 15 posted to Credit Risk by Alan on 12/11/2009 15:33:19

Credit Valuation Adjustment

Filed under: Credit Value Adjustment, CVA

Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation
can be written as

Exposure, Independent of Counterparty Default

Assuming independence between exposure and counterparty’s credit quality greatly simplifies the analysis. Under this assumption this simplifies to

where

which is the risk-neutral discounted expected exposure (EE)

The Function of the CVA Desk and Implications for Technology Solution

CVA Operating Model

- The key considerations for a Front Office CVA desk are:

Charge Model
Hedging Portfolio CVA
Proxy Hedging
Hedge Effectiveness
P&L Attribution/Revaluation of Portfolio

References

1. A Guide to Modeling Counterparty Credit Risk, GARP Risk Review, July/August 200, Steven H. Zhu, Michael Pykhtin.

2. EM RISK, Risk Analytics (Credit Value Adjustment Solution Consultants)

Credit Valuation Adjustment

Alan — Thu, 12 Nov 2009 15:14:52 GMT

Revision 14 posted to Credit Risk by Alan on 12/11/2009 15:14:52

Credit Value Valuation AdjustmentDefined

Filed under: Credit Value Adjustment, CVA

Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation
can be written as

Exposure, Independent of Counterparty Default

Assuming independence between exposure and counterparty’s credit quality greatly simplifies the analysis. Under this assumption this simplifies to

where

which is the risk-neutral discounted expected exposure (EE)

References

1. A Guide to Modeling Counterparty Credit Risk, GARP Risk Review, July/August 200, Steven H. Zhu, Michael Pykhtin.

2. EM RISK, Risk Analytics (Credit Value Adjustment Solution Consultants)

Credit Value Adjustment Defined

Alan — Fri, 04 Sep 2009 13:38:23 GMT

Revision 13 posted to Credit Risk by Alan on 04/09/2009 14:38:23

Credit Value Adjustment Defined

Filed under: Credit Value Adjustment, CVA

Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation
can be written as

Exposure, Independent of Counterparty Default

Assuming independence between exposure and counterparty’s credit quality greatly simplifies the analysis. Under this assumption this simplifies to

where

which is the risk-neutral discounted expected exposure (EE)

References

1. A Guide to Modeling Counterparty Credit Risk, GARP Risk Review, July/August 200, Steven H. Zhu, Michael Pykhtin.

2. ADSATIS Risk Consulting EM RISK, Risk Analytics (Credit Value Adjustment Solution Consultants)

Credit Value Adjustment Defined

Alan — Mon, 06 Jul 2009 12:33:21 GMT

Revision 12 posted to Credit Risk by Alan on 06/07/2009 13:33:21

Credit Value Adjustment Defined

Filed under: Credit Value Adjustment, CVA

Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation
can be written as

Exposure, Independent of Counterparty Default

Assuming independence between exposure and counterparty’s credit quality greatly simplifies the analysis. Under this assumption this simplifies to

where

which is the risk-neutral discounted expected exposure (EE)

References

1. A Guide to Modeling Counterparty Credit Risk, GARP Risk Review, July/August 200, Steven H. Zhu, Michael Pykhtin.

2.Parker-Fitzgerald ADSATIS Risk Consulting, Risk Analytics (Credit Value Adjustment Solution Consultants)

Credit Value Adjustment Defined

Alan — Thu, 04 Jun 2009 09:21:52 GMT

Revision 11 posted to Credit Risk by Alan on 04/06/2009 10:21:52

Credit Value Adjustment Defined

Filed under: Credit Value Adjustment, CVA

Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation
can be written as

Exposure, Independent of Counterparty Default

Assuming independence between exposure and counterparty’s credit quality greatly simplifies the analysis. Under this assumption this simplifies to

This assumes for instance that the risk factors for the CDS and

where

which is the underlying are uncorrelated.risk-neutral discounted expected exposure (EE)

References

1. A Guide to Modeling Counterparty Credit Risk, GARP Risk Review, July/August 200, Steven H. Zhu, Michael Pykhtin.

2. Parker-Fitzgerald Consulting, Risk Analytics (Credit Value Adjustment Solution Consultants)

Credit Value Adjustment Defined

Alan — Thu, 04 Jun 2009 08:13:13 GMT

Revision 10 posted to Credit Risk by Alan on 04/06/2009 09:13:13

Credit Value Adjustment Defined

Filed under: Credit Value Adjustment, CVA

Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation
can be written as

Exposure, Independent of Counterparty Default

Assuming independence between exposure and counterparty’s credit quality greatly simplifies the analysis. Under this assumption this simplifies to

This assumes for instance that the risk factors for the CDS and the underlying are uncorrelated.

References

1. A Guide to Modeling Counterparty Credit Risk, GARP Risk Review, July/August 200, Steven H. Zhu, Michael Pykhtin.

2. Parker-Fitzgerald Consulting, Risk Analytics (Credit Value Adjustment Solution Consultants)

Credit Value Adjustment Defined

Alan — Thu, 04 Jun 2009 07:56:59 GMT

Revision 9 posted to Credit Risk by Alan on 04/06/2009 08:56:59

Credit Value Adjustment Defined

Filed under: Credit Value Adjustment, CVA

Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation
can be written as

Exposure, Independent of Counterparty Default

Assuming independence between exposure and counterparty’s credit quality greatly simplifies the analysis. Under this assumption this simplifies to

This assumes for instance that the risk factors for the CDS and the underlying are uncorrelated.

References

1. A Guide to Modeling Counterparty Credit Risk, GARP Risk Review, July/August 200, Steven H. Zhu, Michael Pykhtin.

2. Parker-Fitzgerald Consulting, Risk Analytics (Credit Value Adjustment Solution Consultants)

3. QuiC, Risk Management Software Vendor (CVA Market Leaders)

Credit Value Adjustment Defined

Alan — Mon, 04 May 2009 09:31:46 GMT

Revision 8 posted to Credit Risk by Alan on 04/05/2009 10:31:46

Credit Value Adjustment Defined

Filed under: Credit Value Adjustment, CVA

Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation
can be written as

Exposure, Independent of Counterparty Default

Assuming independence between exposure and counterparty’s credit quality greatly simplifies the analysis. Under this assumption this simplifies to

This assumes for instance that the risk factors for the CDS and the underlying are uncorrelated.

References

1. A Guide to Modeling Counterparty Credit Risk, GARP Risk Review, July/August 200, Steven H. Zhu, Michael Pykhtin.

2. Parker-Fitzgerald Consulting, Risk Analytics (Credit Value Adjustment Solution Consultants)

3. QuiC, Risk Management Software Vendor (CVA Market Leaders)

Credit Value Adjustment Defined

Alan — Mon, 04 May 2009 09:31:46 GMT

Revision 8 posted to Credit Risk by Alan on 04/05/2009 10:31:46

Credit Value Adjustment Defined

Filed under: Credit Value Adjustment, CVA

Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation
can be written as

Exposure, Independent of Counterparty Default

Assuming independence between exposure and counterparty’s credit quality greatly simplifies the analysis. Under this assumption this simplifies to

This assumes for instance that the risk factors for the CDS and the underlying are uncorrelated.

References

1. A Guide to Modeling Counterparty Credit Risk, GARP Risk Review, July/August 200, Steven H. Zhu, Michael Pykhtin.

2. Parker-Fitzgerald Consulting, Risk Analytics (Credit Value Adjustment Solution Consultants)

3. QuiC, Risk Management Software Vendor (CVA Market Leaders)

Credit Value Adjustment Defined

Alan — Mon, 04 May 2009 09:29:57 GMT

Revision 7 posted to Credit Risk by Alan on 04/05/2009 10:29:57

Credit Value Adjustment Defined

Filed under: Credit Value Adjustment, CVA

Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation
can be written as

Exposure, Independent of Counterparty Default

Assuming independence between exposure and counterparty’s credit quality greatly simplifies the analysis. Under this assumption this simplifies to

This assumes for instance that the risk factors for the CDS and the underlying are uncorrelated.

References

1. A Guide to Modeling Counterparty Credit Risk, GARP Risk Review, July/August 200, Steven H. Zhu, Michael Pykhtin.

2. Parker-Fitzgerald Consulting, Risk Analytics (Credit Value Adjustment Solution Consultants)

3. QuiC. Risk Management Software Vendor

Credit Value Adjustment Defined

Alan — Mon, 04 May 2009 09:28:22 GMT

Revision 6 posted to Credit Risk by Alan on 04/05/2009 10:28:22

Credit Value Adjustment Defined

Filed under: Credit Value Adjustment, CVA

Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation
can be written as

Exposure, Independent of Counterparty Default

Assuming independence between exposure and counterparty’s credit quality greatly simplifies the analysis. Under this assumption this simplifies to

This assumes for instance that the risk factors for the CDS and the underlying are uncorrelated.

References

1. A Guide to Modeling Counterparty Credit Risk, GARP Risk Review, July/August 200, Steven H. Zhu, Michael Pykhtin.

2. Parker-Fitzgerald Consulting, Risk Analytics

3. QuiC.

Credit Value Adjustment Defined

Alan — Wed, 22 Apr 2009 11:53:01 GMT

Revision 5 posted to Credit Risk by Alan on 22/04/2009 12:53:01

Credit Value Adjustment Defined

Filed under: Credit Value Adjustment, CVA

Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation
can be written as

Exposure, Independent of Counterparty Default

Assuming independence between exposure and counterparty’s credit quality greatly simplifies the analysis. Under this assumption this simplifies to

This assumes for instance that the risk factors for the CDS and the underlying are uncorrelated.

References

1. A Guide to Modeling Counterparty Credit Risk, GARP Risk Review, July/August 200, Steven H. Zhu, Michael Pykhtin.

Credit Value Adjustment Defined

Alan — Wed, 22 Apr 2009 11:42:24 GMT

Revision 4 posted to Credit Risk by Alan on 22/04/2009 12:42:24

Credit Value Adjustment Defined

Filed under: Credit Value Adjustment, CVA

Credit value adjustment (CVA) is by definition the difference between the risk-free portfolio value and the true portfolio value that takes into account the possibility of a counterparty’s default. In other words, CVA is the market value of counterparty credit risk.

Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation
can be written as

References

1. A Guide to Modeling Counterparty Credit Risk, GARP Risk Review, July/August 200, Steven H. Zhu, Michael Pykhtin.

Credit Value Adjustment Defined

Alan — Wed, 22 Apr 2009 11:38:35 GMT

Revision 3 posted to Credit Risk by Alan on 22/04/2009 12:38:35

Credit Value Adjustment Defined

Filed under: Credit Value Adjustment, CVA

Credit value adjustment (CVA) is by definition the difference between the risk-free portfolio value and the true portfolio value that takes into account the possibility of a counterparty’s counterparty’s default. In other words, CVA is the market value of counterparty credit risk.

References

1. A Guide to Modeling Counterparty Credit Risk, GARP Risk Review, July/August 200, Steven H. Zhu, Michael Pykhtin.

Credit Value Adjustment Defined

Alan — Fri, 10 Apr 2009 08:55:21 GMT

Revision 2 posted to Credit Risk by Alan on 10/04/2009 09:55:21

Credit Value Adjustment Defined

Filed under: Credit Value Adjustment, CVA

References

1. A Guide to Modeling Counterparty Credit Risk, GARP Risk Review, July/August 200, Steven H. Zhu, Michael Pykhtin.