Credit Derivatives: Introduction to CDS and Credit Risk Basics

Question 1

What are credit derivates?

Answer 1

Credit derivatives are contracts where the payoff depends on the creditworthiness of one or more subjects (usually large companies or countries)

Main contract of focus credit default swaps

Question 2

How does a credit default swap work?

Answer 2

1. The protection buyer pays a CDS premium to the protection seller.
   * The premium is usually paid periodically until either the end of the contract maturity or a credit even occurence
2. The protection seller pays the buyer in case the specified credit event occurs.
   * When a credit event occurs, the CDS contract specifies either a physical delivery of the bonds or a cash payment (dpending on the agreement between parties)
   * In the case of physical delivery, if there is a credit event the buyer has the right to sell the bond issued by the company at its face value

Question 3

What is the recovery rate for a bond?

Answer 3

Recovery rate for a bond is usually defined as the price of the bond immediately after default as a percent of its face value.

Question 4

What default probability is used when pricing CDS?

Answer 4

1. We use unconditional default/survival probabilities
2. We use risk-neutral probabilities rather than historical

Question 5

How do we express survival rate V(t) of a company in continuous time?

Answer 5

1. We express V(t) as an exponential function with a hazard rate.
2. Define Hazard rate λ(t) (or Default Intensity) at time t as the rate such that λ(t) * Δt is the conditional probability of default between t and t +Δt
3. Take the integral for smaller and smaller periods
4. The V(t) becomes V(t) = e^-λbar(t)t and cumulative default probability becomes 1- e^-λbar(t)t, where λbar(t)t is the average hazard rate between 0 and t

Question 6

What is the bond yield spread?

Answer 6

Bond yield spread is the excess of the bond’s yield over the risk-free rate.

Question 7

How to determine default probabilities from bond’s yield spread?

Answer 7

1. Given a bond with a certain maturity T, spread per annum s(T), a recovery rate equal to R and an average hazard rate of λbar(t)
2. The average expected loss of the bond is also equal to λbar(t)(1-R)
3. If the spread of the bond s(T) is seen as the average expected loss:
   λbar(t) = s(T)/(1-R)

If we want the average Hazard rate for a particular year (for example year 3 from 3-year yield spread and 2 year yield spread) we multiply the cumulative (year 1, 2, and 3) average hazard rate by 3 (number of years) and subtract the cumulative average hazard rate for years 1 and two and multiply by 2