Hull Chapter 23 - Credit Risk

Question 1

Define Hazard Rates

Answer 1

The hazard rate λ(t) is then defined so that λ(t)Δt is the probability of default between time t and t+Δt conditional on no earlier default.

Question 2

Define recovery rates

Answer 2

Bond’s market value a few days after a default, as a percentage of its face value. Recovery rates are significantly negatively correlated with default rates.

Question 3

Why do estimates of default probability from historical data much lower than estimates based on bond prices?

Answer 3

Risk-neutral estimates are larger because of one or more of the following sources of
positive risk-adjustments:

• Liquidity Premium — Corporate bonds are relatively illiquid and so there may be a liquidity risk premium.
• Conservatism — Bond traders use subjective default probabilities that exceed the historical estimates
• Skewness — Bond returns are skewed (limited upside, large downside) and therefore it is more difficult to diversify the risk in a bond portfolio.

Question 4

So which rates should be used, the real world or the risk neutral ones?

Answer 4

If the goal is to price a bond or value a credit derivative, the risk neutral default rates should be used.

if we want to make probabilistic statements about the cash flows then we have to use real world probabilities.

Question 5

Three clauses in derivative contracts that are often used to mitigate exposure to credit risk include the following:

Answer 5

• Netting — If the counterparty defaults on one transaction, then they must default on all transactions with that counterparty. This prevents them from selectively defaulting on transactions where they owe money but keeping alive other derivative transactions in which they are owed money.
• Collateral Requirements — Requirements for a counterparty to post collateral in the form of cash or marketable securities in the amount of their potential losses from one or more transactions.
  
  • Limit: the amount is not protected and if a company defaults then the counterparty many not be able to collect
• Downgrade Triggers — These are conditions included in contracts that force an early termination of the transaction if the counterparty credit rating drops below a threshold.
  
  • But if the counterparty defaults and has several contracts that have downgrade triggers they may not be able to close out all of their contracts