R.38 Credit Default Swaps

Question 1

CDS calculations

1. Expected Loss
2. Upfront payment (buyer)
3. Upfront premium
4. Profit for protection buyer%

Answer 1

Calculations

1. Expected Loss_t = (hazard rate)_t x (loss given default)_t
2. Upfront payment = (PV_{protection leg}) - (PV_{premium leg})
   
   • ​​If cpn pmt is not set = credit spread of reference obligation…then upfront pmt from one counterpartyto other is needed.
3. Upfront premium (%) ≈ (CDS_spread - CDS_coupon) x CDS_duration
   
   • ​​fs1
4. Profit (protection buyer) ≈ change in spread (bps) x CDS_duration x notional principal
   
   • _{<span>​​fs2 ​</span>}

Question 3

Why swap rate curve preferred as benchmnark interest rate curve?

• Swap rates reflect?
• Swap market regulation?
• Swap curve quotes?

Answer 3

The swap rate curve provides a benchmark measure of interest rates. It is similar to the yield curve except that the rates used represent the interest rates of the fixed-rate leg in an interest rate swap.

Market participants prefer the swap rate curve as a benchmark interest rate curve rather than a government bond yield curve for the following reasons:

• Swap rates reflect the credit risk of commercial banks rather than governments.
• The swap market is not regulated by any government.
• The swap curve typically has yield quotes at many maturities.

Institutions like wholesale banks are familiar with swaps and, as a result, often use swap curves (rather than other interest rate benchmarks) to value their assets and liabilities.

swap spread = (swap rate) – (Treasury bond yield)

• We define swap spread as the additional interest rate paid by the fixed-rate payer of an interest rate swap over the rate of the “on-the-run” government bond of the same maturity.

Question 4

CDS Terminology

• Pricing input variables
• Hazard rate
• CDS CPN rates
• CDS long vs short positions

Answer 4

Terminology

Pricing input variables

1. probability of default
2. loss given default
3. CPN rate on swap

Hazard rate

• is conditional probability of default (probablity of default given default has not occured).

CDS CPN rates

• CDS coupon rates are standardized, with the most common coupons being either 1% or 5%.
  
  • 1% = investment-grade company or index
  • 5% = high-yield company or index

CDS long/short positions

• CDS Seller is Long CDS / Long credit risk b/c they want positive outcome (no default)
• CDS Buyer is Short CDS / short credit risk b/c they benefit from bad/negative outcome (defaulting)
• Because the credit protection buyer promises to make a series of future payments, it is regarded as being short. This is consistent with the fact that in the financial world, “shorts” are said to benefit when things go badly. Credit quality is based on the underlying debt obligation, and when it improves, the credit protection seller benefits. When credit quality deteriorates, the credit protection buyer benefits. Hence, the CDS industry views the credit protection seller as the long and the buyer as the short. This point can lead to confusion because we effectively say the credit protection buyer is short and the credit protection seller is long.

Question 5

CDS

• Definition and payment structure

Answer 5

Credit default swap is a derivative contract between two parties, a credit protection buyer and credit protection seller, in which the buyer makes a series of cash payments to the seller and receives a promise of compensation for credit losses resulting from the default—that is, a pre-defined credit event—of a third party.

Question 6

Cheapest to deliver obligation

Answer 6

Question 7

Credit events

Answer 7

Credit event: the outcome that triggers a payment from the credit protection seller to the credit protection buyer. This event must be clear and unambiguous.

3 General Types:

1. Bankruptcy: declaration provided for by a country’s laws that typically involves the establishment of a legal procedure that forces creditors to defer their claims. If bankruptcy pmt plan fails, there is likely to be a full liquidation of the company, at which time the court determines the payouts to the various creditors. Business as normal unless goes to full liquidation.
2. Failure to pay: occurs when a borrower does not make a scheduled payment of principal or interest on any outstanding obligations after a grace period, without a formal bankruptcy filing. Late PMT within grace period is OK.
3. Restructuring (non-US companies): Must be involuntary, meaning that it is forced on the borrower by the creditors who must accept the restructured terms. Refers to a number of possible events, including:
   
   • reduction or deferral of principal or interest,
   • change in seniority or priority of an obligation, or
   • change in the currency in which principal or interest is scheduled to be paid.

US doesn’t consider resctructuring a credit event b/c bankruptcy is preferred. Europe prefers restructuring (think Greek Debt Crisis).

Who determines if its a credit event?

• _DC within ISDA (_International Swaps and Derivatives Association): 15-member group called Determination Committee (DC)