# Week 7: CDS, Stress Testing and CVA/DVA

### Week 7: CDS, Stress Testing and CVA/DVA

#### Summaries

• Week 7: CDS, Stress Testing and CVA/DVA > Lesson 1: CDS and CDS Spreads > Video Lesson
• Week 7: CDS, Stress Testing and CVA/DVA > Lesson 2: Stress Testing > Video Lesson
• Week 7: CDS, Stress Testing and CVA/DVA > Summary > Summary and Goodbye
• Week 7: CDS, Stress Testing and CVA/DVA > Bonus Class: CVA and DVA > Video

#### Week 7: CDS, Stress Testing and CVA/DVA > Lesson 1: CDS and CDS Spreads > Video Lesson

• We will see that we can use CDS, that is the acronym for credit default swaps, for estimating the probability of default of a counterparty.
• When we consider a CDS, the company subject to default is known as the reference entity, and its default is the so-called credit event.
• The buyer of a CDS buys the right to sell the bonds issued by the reference entity for their face value, if the reference entity defaults.
• With the term notional principal, we indicate the total face value of all the bonds, which are part of the CDS. In a CDS, the buyer usually makes periodic payments to the seller, until the end of the life of the CDS, or until a credit event happens.
• The notional principal is 100 million euros and the buyer agrees to pay 90 basis points per year, in quarterly arrears.
• By definition, the CDS spread is simply the total amount paid every year by the buyer as a percent of the nominal principal.
• The CDS spread is 0.9%. This spread is the nothing more than the extra rate required by the seller of the CDS to bear the risk of default of the reference entity.
• CDS spreads can be used to rapidly estimate the probability of default of a counterparty.
• At the numerator we have the CDS spread, and at the denominator we have one minus the recovery rate.
• Very simple and very very quick for a first estimate of the probability of default of a counterparty.
• Credit spreads can also been combined to obtain the so-called intermediate PDs. Suppose that, for the same reference entity, the 3-year CDS spread is 50 bps, while the 5-year CDS spread is 60 bps.
• The recovery rate is assumed to be 60%. Using the previous formula we can easily compute the average probability of default over 3 and 5 years.
• These probabilities can then be used to estimate the average probability of default between year 3 and year 5, which is more or less 1.88%. The trick is to use the general formula you see on your screen.

#### Week 7: CDS, Stress Testing and CVA/DVA > Lesson 2: Stress Testing > Video Lesson

• Hi there, if you have read financial newspapers in the last months, you have probably read about stress testing.
• What is stress testing? You have probably read about the fact that now, under Basel III, banks are required to perform stress testing, in order to take into account the risk of extreme events.
• The aim of this class is to introduce you to stress testing.
• A stress test is a procedure, a way to determine the ability of a given financial institution, typically a bank, to cope with an economic crisis, or bad economic conditions, in general.
• Using stress testing, a bank must answer questions like: what happens if interest rates increase by at least x%? what happens if the correlation among defaults increases? And so on.
• Thanks to Basel III, stress testing has become increasingly important.
• A stress testing procedure is usually based on the so-called scenarios.
• A scenario is simply a given configuration of parameters and variables for the model we use in assessing risk.
• We want to see what happens to our risk measures and capital requirements under particularly stressed conditions.
• From an operative point of view, stress testing is performed using computational and statistical tools, such as Monte Carlo simulations, extreme value theory and, as the statisticians among you may guess, sensitivity analysis.
• We can use a simple example to give an idea of how stress testing works.
• Then the 1-year probability of default is 5.57%. A simple scenario is to assume that sigmaV increases to 0.5, or 0.8, or even 1.0 and see what happens to the PD. Using the three values of sigmaV, we see that the probability of default of our counterparty dramatically increases.
• Historical evidence means that we want to test how we are able to cope with extreme scenarios we have already observed in the past.
• When dealing with expert judgments, we want to test hypotheses developed by economists about future trends and cycles.
• For example it has become rather common in Europe, where the ECB really insists on stress testing.
• Apart from scenario analysis, another way of performing stress testing is to use the so-called stressed measures of risk.
• Developed for Market Risk, Stressed VaR, also known as S-VaR, is now popular in Credit Risk as well.
• A simple example in R is the best way to understand stressed value-at-risk.
• Assume we know that our losses are lognormally distributed with mean 1 and standard deviation 2.

#### Week 7: CDS, Stress Testing and CVA/DVA > Summary > Summary and Goodbye

• In this course, we have seen many new interesting things – at least I hope – together.
• We have defined credit risk, and we have contextualized credit risk in the Basel framework.
• Now, you are able to estimate the PD of a counterparty, using different techniques, from credit rating to credit spreads, and to more advanced techniques, such as Merton’s-like models.
• If you are interested in credit risk, you now have the bases to continue your studies.
• Maybe TU Delft will offer a new more advanced course on this topic.
• The video lessons end today, but in the next weeks we will continue answering your questions on the course forum, and I will prepare new answer videos, because now I have more time for that.
• If you have suggestions about improvements, please feel free to tell us on the course forum.

#### Week 7: CDS, Stress Testing and CVA/DVA > Bonus Class: CVA and DVA > Video

• Counterparty credit risk is the risk arising from the possibility that the counterparty may default on amounts owned on a transaction.
• In simple terms: it is the risk that my counterparty will default before the expiration of its contractual obligations.
• Credit Valuation Adjustment, or CVA, is nothing more than the market value of counterparty credit risk from the point of view of the ?buyer?
• When dealing with a security, it can be quantified as the difference between the risk-neutral value and the ?true value?, that is the value taking into account the possibility of the counterparty default.
• The risk-neutral value of a security is the value we can compute under the risk-neutral measure.
• In financial mathematics, we speak of risk-neutrality, if a probability measure is such that the today?s value of each security is nothing more than the discounted expected value of the same security at maturity.
• The computation of CVA is not at all simple: it involves cumbersome mathematical formulas and a lot of computer simulations.
• It represents counterparty credit risk from the point of view of the ?seller?, which takes into account its own default, and the impact of this on the value of the transaction.
• DVA is a highly controversial measure, and regulators are very suspicious about its use by banks.
• Given the true value of a derivative, if we remove CVA and DVA what remains is the risk-neutral value.
• If the PD of A increases, the value of its bonds decreases.
• Default may not be a negative event, if we just focus our attention on the single transaction, and not on A as a whole.
• In case of default, A is no longer supposed to make any payment to B. ?This is a gain for A, and this is why DVA increases when PD and credit spreads increase.