Chapter 8: Credit VaR

Question 1

What are credit losses determined by?

Answer 1

• Probability of default (PD) or more generally a change in credit rating
• Credit exposure (CE) or exposure at default (EAD)
• Loss given default (LGD) or recovery rates (f)

Characteristic of the credit loss distribution is that it is highly skewed distribution

Question 2

What is the challenge in defining credit loss distribution?

Answer 2

• Challenge: combine these (stochastic) credit risk drivers (PD, CE and LGD) into a credit loss distribution
• This is clearly very complex, and thus we need to impose a structure on the marginal distributions of the risk drivers, and/or structure on the joint distribution.
• In principle, all three risk drivers are random variables, but often simplifying assumptions are made:
  
  1. all risk drivers are independent; or even stronger
  2. credit exposure and recovery rates are deterministic

Question 3

What is the diversification of credit risk?

Answer 3

• By aggregating numerous instruments in a portfolio, we can realize diversification benefits.
• While expected losses are not impacted, the loss distribution of the portfolio can be very different from the loss distribution of a single instrument.
  
  • Key element: correlation between default probabilities.
  • More generally: PDs are dependent, such that the dispersion of credit losses and the joint probabilities depend on this correlation.

Question 4

What is credit VaR?

Answer 4

• Based upon a credit loss distribution, we can compute a credit VaR. Such VaR is the credit P&L that will not be exceeded with certain confidence level over a target horizon.
• Since the target horizon is often longer term, the time-value of money becomes relevant: credit VaR is therefore always computed as a relative VaR (and not an absolute VaR).
• VaR = unexpected credit loss, provisions are made for expected losses.

Question 5

What are the credit VaR parameters?

Answer 5

• Choice of horizon and confidence level is determined by the purpose of the VaR measure.
• If the purpose of the credit VaR is to define economic capital the institution needs to hold on:
  
  • Horizon equals the longer 1 year horizon, corresponding to a typical loan evaluation frequency
  • Confidence level is set at at high 99,9% level = corresponding to the Basel III requirement.

Question 6

What accounts for the complexity of credit risk measurement?

Answer 6

• The above examples are highly simplified, and do not really show the complexity of credit risk measurement:
  
  1. We should allow for more general credit events, not just default: any downgrade of a bond also results in a credit loss
  2. We should allow for correlations across obligors of all these credit quality changes: only then benefits of diversification and costs of concentration are accounted for
  3. We should come up with a proper credit exposure estimate and recovery rate estimate

Question 7

What are credit risk models?

Answer 7

• This complexity in modelling credit risk at a portfolio level makes that much effort has gone at developing credit risk portfolio models.
• 4 leading models:
  
  1. CreditMetrics developed by J.P. Morgan
  2. CreditPortfolioView from McKinsey
  3. KMV from Moody’s KMV corp.
  4. CreditRisk+ developed by Credit Suisse
• All these models use very different approaches and thus different building

blocks

Question 8

What is CreditMetrics?

Answer 8

• Has been developed by JPMorgan.
• Key charachteristics:
  
  • Portfolio approach: allows for consolidation of credit risk across large portfolios of credit sensitive instruments: eg. bonds, loans and derivatives
  • It simulates a credit loss distribution that accounts for updrages, downgrades and defaults.

Question 9

How does the CreditMetrics work?.

Answer 9

• To model the change in value due to credit quality migration we need to revalue the bond in either credit quality state:
  
  • Revalue the bond in the case of default based on recovery rates
  • Revalue the bond in case of an up- or downgrade by using rating-specific discount rates
• To revalue the bond in case of default, we can use recovery values in function of the seniority of the instrument
• To revalue the bond in case of a up- or downgrade, we use forward zero-curves per rating category
  
  • These forward values can now be combined with their probabilities of occurence to yield a distribution of future bond values
  • Furthermore, we can easily transform this distribution into a distribution of credit losses by looking at the difference with the expected value
• From this distribution of credit losses we can compute the credit VaR over a 1-year horizon as the worst loss observed at the percentile c.

Question 10

How do we use CreditMetrics for a portfolio?

Answer 10

• When analyzing credit risk losses of a portfolio, we need to account for any dependencies in the rating outcomes of different obligors; such dependency is an empirical fact as obligors are affected by the same economic factors
• Modeling the credit loss distribution of a portfolio therefore requires the estimation of the joint likelihood of migrations

Question 11

Are migrations cross obligors correlated?

Answer 11

• In reality, however, migrations across obligors will typically be correlated.
• One way to infer information on credit quality correlations is to analyze correlations between corresponding stock prices.
• This approach is motivated by the Merton model that allows us to link firm asset values (proxied by equity values) to changes in firm credit quality: if the value of assets falls below the value of liabilities, the firm will be unable to meet its obligations and default
• Whereas the standard Merton model computes the point of default, we can extend the intuition of the Merton model to include all credit migrations.
• To extend the Merton model to reflect any up-or downgrade of the bonds
  
  • We plot a normal distribution of firm value returns and divide its distribution in bands such that bond migration frequencies are reflected
  • Each level of asset value returns, corresponds to a bond value with a particular credit quality

Question 12

What are the simplifying assumptions that are made?

Answer 12

• In principle, all three risk drivers are random variables, but often simplifying assumptions are made:
  
  • all risk drivers are independent; or even stronger
  • credit exposure and recovery rates are deterministic

Question 13

What are the steps of the CreditMetrics?

Answer 13

• CreditMetrics calculates credit value at risk in three/four consecutive steps:
  
  1. Compute the likelihood of the different credit events that are possible: to this end, we use rating migrations that can be derived from a transition matrix.
  2. Compute the corresponding value of the instrument for each different credit event (upgrade, downgrade, default): these values can be derived from credit spread data and recovery values
  3. Compute the credit losses caused by these credit events as compared to the expected credit losses
  4. In case of a portfolio context: 4. Compute the joint migrations for the portfolio of instruments.

Question 14

Why is the incorporation of correlation so complex in credit risk modelling?

Answer 14

Unfortunately, incorporating such correlation is one of the more complex elements in credit risk modelling:

• Data from which this information can be observed is sparse and of poor quality (actual ratings and default correlations, and bond spread correlations)
• Models that infer these correlations from more readily-observable data impose ambitious assumptions in converting the available data (equity price correlations) to the desired data (PD correlations)