Credit Default Swaps

In this lesson, we we introduced to credit default swaps.  We were introduced to how credit default swaps give us information about default probability and how these quantities can be used for hedging, investment, and speculation.

The seller of a credit default swap agrees to compensate the buyer in the event of a loan default or some other credit event on a reference entity in return for periodic premium payments.
The buyer pays period payments of d*S*N where:

• N is the notional principle amount of credit protection
• S is the coupon or the spread and
• d is a fraction of a year (d*S is the total coupon that has accumulated over the years)

this keeps on going until some credit event happens (usually a default).  At the next coupon date after this happens, the buyer has to pay the accrued interest d*S.  Also, the seller has to pay (1-R)*N where R is the recovery rate.  

Example:

Consider a 2-year CDS on a notional amount of $1 million with a spread S of 160 basis points (1.6%) and quarterly premium payments. 

Suppose a default occurs in month 16 of the 24 month protection plan and the recovery rate, R, is 45%.

The buyer:

The buyer pays fixed premiums in months 3,6,9,12,15 = (S*N)/4 = $4000

The accrued interest in month 18 (the next coupon date) is (S*N)/12 = $1333.33

The seller:

The default contingent protection payment in month 18 = (1-R)*N = $550,000

The basic model for CDS cash flows is as follows:

Let {t(k) = delta*k = 1,...,t(n)} denote the time of the coupon payments.  For quarterly payments delta = 1/4

If the reference entity is not in default at time t(k), the buyer pays the premium delta*S*N

If the reference entity defaults at time tau contained in (t(k-1), t(k)], then the contract terminates at time t(k).  The buyer pays the accrued interest (t(k) - tau)*S*N and the buyer receives (1-R)*N.  In the last example, the contract terminated at month 18 since default occurred at time tau=16 months between month 15 and month 18.

We then learned about CDS contract details.  CDS contract details were standardized by the International Swaps and Derivatives Association in 1999.  Changes were made in 2003, and 2009, and may happen again if CDS derivates lead to a financial global recession again.  There are so many different details in a contract because there are many difficult issues: how to determine if a credit event occurred, the recovery rate, the spread set for different bonds, when the coupon is paid (advance vs. arrears), and how the spread is quoted.  

The CDS spread S is approximates (1-R)*h where h is the hazard rate, or the conditional probability of default.  For fixed R, CDS spreads are directly proportional to the hazard rate h.  Thus CDS spreads, along with the recovery rate can help determine what the probability of default is for a given defaultable bond.

We then learned about the development and application history of CDS as well as their impact on the financial crisis and the sovereign debt crisis.  I have omitted this portion from this post.