Lecture 6

Question 1

What is credit risk?

Answer 1

The risk that borrowers and, in general, the counterparty of the transaction, may default or not honour their contractual obligations.

Question 2

What are the 3 ways we can estimate default probabilities?

Answer 2

1) Using historical data.
2) Using credit spreads (bond prices).
3) Using the Merton’s model (equity prices).

Question 3

Do default probabilities always increase overtime?

Answer 3

It depends.
For a company that starts with a good credit rating default probabilities tend to increase with time.
For a company that starts with a poor credit rating default probabilities tend to decrease with time.

Question 4

What is the conditional default probability?

Answer 4

The probability of default for a certain time period conditional on no earlier default.

Question 5

What is the unconditional default probability?

Answer 5

The probability of default for a certain time period as seen time zero.

Question 6

How can we calculate the bond’s yield spread?

Answer 6

The difference in yield between a corporate bond and the risk-free rate.

Question 7

What is the recovery rate?

Answer 7

Bond’s market value a few days after a default, as a percent of its face value.
Higher R, the higher the ‘quality’ of the bond. The correlation with the default rate is significantly negative.

Question 8

How can we calculate the average loss rate at time t? And to what should this approximately equal?

Answer 8

avgHR(1-R). It should equal to the credit spread, since credit spread can be seen as a compensation for the loss rate.

Question 9

What is the more precise method of estimating hazard rates?

Answer 9

The bootstrap method, where we work forward in time choosing hazard rates that match bond prices.

Question 10

Describe the procedure of the bootstrap method.

Answer 10

1) Get the price of the bond with the risk-free rate.
2) Get the price of the bond with the bond yield.
3) Compute spread as the difference in prices between the two.
4) Calculate the PV of Expected loss in each year: PV of (rf bond value - recovery amount).
5) Sum the PV of Expected losses.
6) Compute default probability: Q = spread/sum(PV of Expected losses)

Question 11

How can we get risk-neutral probabilities?

Answer 11

From bond prices or credit default swaps. They assume that expected default losses can be discounted at risk-free rate.

Question 12

How can we get the real world default probabilities?

Answer 12

From historical default probabilties.

Question 13

Usually, the risk-neutral default probability is larger than the real world default probability. Why?

Answer 13

This is the risk premium due to:
1) Liquidity: rf bonds are much more liquid than risky ones.
2) Period analysed: can be over optimistic/depressed, thus impacting subjective default probabilities.
3) High correlation: when a risky bond defaults there is a possibly high risk that other risky bonds in the same sector might default. Called credit contagion. Systemic risk cannot be diversified away.
4) high skewness and limited upside - low diversification - non-systemic risk difficult to diversify away.

Question 14

What is the main problem from using data from credit rating agencies? And what is a possible solution?

Answer 14

Data of credit rating agencies is infrequently updated. Possible solution is to use the equity market - Merton’s model.

Question 15

Describe Merton’s model.

Answer 15

It regards the equity as an option on the assets of the firm. In a simplified setting, equity value is max(V-D,0).Thus, equity value can be computed as a call option.

Question 16

What is the main problem (2 variables) with the Merton’s model? How can we solve it?

Answer 16

Firm value and its volatility are not directly observable. If a company is listed we know its market cap (equity value) and its stock volatility. For there we can estimate both firm value and firm volatility, through Ito Lemma. To calculate it we need a numerical technique to solve the system of 2 equations with 2 unknowns.

Question 17

What does N(-d2) represent in Merton’s Model?

Answer 17

It represents the probability of default - the probability that the debt will be greater than the value of the company in one year.

Question 18

How can we calculate the expected loss on the debt?

Answer 18

EL= (PV of debt - (V-E))/PV of debt

Question 19

How can we calculate the recovery rate in Merton’s Model?

Answer 19

RR = 1 - EL/N(-d2)

Question 20

What are the main issues of the Merton model?

Answer 20

1) Gaussianity.
2) Risk-neutral probabilities.
3) Debt can only expire at time T.

Question 21

Which model overcomes the issues of the Merton model? What is it based upon?

Answer 21

Expected Default Frequency model (probability that a given firm will default within 1 year), based upon the distance to default (DD), which is the number of STD from default of a firm (a modification of -d2).

Question 22

What is the Credit Value Adjustment (CVA)?

Answer 22

It is the amount by which a dealer must reduce the total value of transactions with a counterparty because of counterparty default risk.

Question 23

What are the 3 cases of CVA?

Answer 23

1) Contract is always a liability (short options) - NO credit risk. No adjustment needed.
2) Contract is always an asset (long options) - always credit risk. We need adjustments.
3) Contract can become either an asset or a liability (forward) - possible credit risk.

Question 24

How can CVA be calculated?

Answer 24

CVA = sum (qi(1-R)*vi)
where v is the today value of the derivative in consideration and qi is the risk-neutral probability of default at time i.

Question 25

What is the adjusted value for the derivative allowing for possible defaults?

Answer 25

f0/f0 = B0/B0 = f0exp^(-T(y-y)
where y and y are the yield of a risk-free zero coupon bond B=e^(-yT) and the yield of the company ZCB B= e^(-yt) both maturing at T

Question 26

What are the 4 members (in addition to CVA) of the XVA: X-Value Adjustment?

Answer 26

1) Debt Valuation Adjustment (DVA): like CVA but accounts for the institution’s own default risk.
2) Funding Valuation Adjustment (FVA): difference between the rate paid for the collateral to the bank’s treasury and the rate paid by the clearing house.
3) KVA: adjustment for regulatory capital through the life of the contract.
4) Margin Valuation Adjustment (MVA): adjustments for initial margin and variation margin do to MM provision.

Question 27

What is default correlation? Why does it exist?

Answer 27

Credit default correlation is a measure of the tendency of two companies to default both at about the same time. It exists because companies in same industry/region/area are usually affected by the same source of risk at the same time.

Question 28

How can we measure default correlation?

Answer 28

No generally accepted measure. The most famous model is the Gaussian copula model. It assumes that all companies will default eventually, and try to measure the correlation between the probability distributions of the time to default for more than 2 companies.

Question 29

What is copula used for? What does Gaussian copula model do?

Answer 29

Copula is used to describe the dependence among variables.
Gaussian copula model quantifies the joint probability of default. It analyses the correlation of the probability distribution times to default of n different firms.

Question 30

What is the main trick of the Gaussian Copula Model when dealing with high non-normality of the pdf?

Answer 30

Making them normal so a unique correlation parameter can determine the join probability of default. This is the ‘percentile to percentile’ transformation.
This is the copula correlation.
Forcing the normality, we can now jointly analyse something that is non-normal through a multivariate normal and unique correlation.

Question 31

Gaussian copula model aka ‘the formula that killed Wall Street’… Explain what happened.

Answer 31

Banks started using and abusing the method because it saved a lot of time. If the copula number was low, banks just assumed no risk and didn’t try to understand the underlying and sold these products (CDO tranches). After 6/7 years everything went wrong. The main problem was the imposed Gaussian correlation for strongly non gaussian quantities (risk). The model was hypersensitive to changes in the underlying assumptions (correlation parameters).

Question 32

Why is the Gaussian Copula Model not appropriate for many finance applications?

Answer 32

It is statistically and financially NOT robust.

Question 33

What is Credit VaR?

Answer 33

It is the maximum loss level given a certain confidence level that we will not exceed over a certain period of time.

Question 34

What is the main purpose of credit derivatives?

Answer 34

To transfer credit risk to a third party.

Question 35

What is a Credit Default Swap?

Answer 35

Insurance against default. Buyer of the instrument acquires protection form the seller against a default by a particular company or country (the reference entity).

Question 36

What happens in the case of default in a CDS?

Answer 36

The buyer had the right to sell bonds at their face value to the seller who then incurs the loss.

Question 37

What is recovery rate?

Answer 37

The ratio of the value of the bond issued by reference entity immediately after default to the face value of the debt.

Question 38

Why are CDSs so attractive?

Answer 38

1) They allow credit risks to be traded in the same way as market risks.
2) They are a proxy for default.
3) They can be used to transfer credit risks to a third party.
4) They can be used to hedge a bond position and can make a risky bond almost risk-free.

Question 39

What are the 4 steps to value a CDS?

Answer 39

1) Calculation of the unconditional default and survival probabilities.
2) Calculation of PV of expected payments.
3) Calculation of PV of expected payoffs.
4) Calculation of PV of accrual payment made in event of a default.
Final goal is to find s, the CDS spread.

Question 40

What is an Asset Backed Security (ABS)?

Answer 40

It is a group of securities created from a portfolio of loans, bonds, credit card receivables, mortgages…. where the income from the assets is tranches. A ‘waterfall’ structure defines how income is first used to pay the promised return to the senior tranches, then to the next most senior tranche (mezzanine) and so on (equity tranche).

Question 41

Define the losses, risks and expected yields of the 3 ABS tranches.

Answer 41

Senior tranche: last loss, lowest risk, lowest expected return.
Mezzanine tranche: second loss, medium risk, medium expected return.
Equity tranche: first loss, highest risk, highest expected return.

Question 42

What is a cash CDO?

Answer 42

is an ABS in which the underlying assets are debt obligations.

Question 43

What is CDO^2?

Answer 43

Is a CDO on a CDO (created from mezzanine tranche). Similar to ABS CDO.

Question 44

What is a synthetic CDO?

Answer 44

Similar to regular CDO in terms of structure but with short CDS contracts.

Question 45

What are 2 crucial things that have been misunderstood about ABSs and CDOs?

Answer 45

1) That correlation goes up in bad moments, as such also the default correlations and all products/institutions among them.
2) Recovery rates go down in bad moments.