Ch6 Credit Derivatives (1)

1. Credit Default Swaps
The most poplular credit derivatives
1-1. Terminology
- reference entity
- credit event
- notional principal: par value
- CDS spread
- settlement

1-2. Credit Default Swaps & Bond Yields
The n-year CDS spread should be approximately equal to the excess of the par yield on an n-year corporate bond over the par yield on an n-year risk-free bond.
- if CDS spread less than the difference: buying assets & buying protection
- if CDS spread greater than the difference: borrowing @risk-free, shorting & selling CDS protection

**CDS Spread = Risk-free rate; approximately equal to (LIBOR/Swap - 10 basis points)

1-3. Cheapest-to-Diliver (CTD) Bond
In the event of default, the protection buyer choose for delivery the bond that can be purchased most cheaply.
e.g.) the most recent settlement price = 93_08
Bond 1: quoted price = $99.50, conversion factor = 1.0382
Bond 2: quoted price = $143.50, conversion factor = 1.5188
Bond 3: quoted price = $119.75, conversion factor = 1.2615

2. Valuation of Credit Default Swaps
Step 1: Calculate P.V. of expected payment
Step 2: Calculate P.V. of expected payoff in the event of default
Step 3: Calculate P.V. of accrual payment in the event of default
Step 4: Calculate CDS spread

2-1. Marking to Market a CDS
e.g.) CDS spread = 150 basis points, P.V. of expected payments = 4.1130 x CDS spread, P.V. of expected payoff = 0.0511 per $
=> P.V. of expected payments = 4.1130 x .0150 = 0.0617 per $
0.0617 - 0.0511 = 0.0106 per $
Mark-to market value of swap to buyer of protection = -0.0106 per $

2-2. Estimating Default Probabilities
The default probabilities used to value a CDS should be risk-neutal default probabilities.

2-3. Binary Credit Default Swaps
A binary credit default swap is structured similarly to a regular CDS except that the payoff is a fixed dollar amount.

3. Credit Indices
- CDX NA 1G: a portfolio of 125 investment grade companies in North America
- iTraxx Europe: a portfolio of 125 investment grade names in Europ


4. CDS Forwards & Options
4-1. Forward CDS: obligation to buy or sell a particular CDS on a particular reference entity at a particular future time T.

4-2. CDS option: option to buy or sell a particular CDS on a particular reference entity at a particular future time T


5. Baset CDS
- add-up basket CDS
- first-to-default CDS & nth-to-default CDS

6. Total Return Swaps (TRS)
- TRS buyer (protection seller): Total return + Depreciation Amount
- TRS issuer (protection buyer): LIBOR + spread

7. Asset-Backed Security (ABS)

8. Collateralized Debt Obligations (CDOs)
8-1. Cash CDOs

8-2. Synthetic CDOs

8-3. Single Tranche Trading
The market uses CDS indices portfolios to define standard CDO tranches. The trading of these standard tranches is know as single tranche trading.
A single tranche trade is an agreement where one side agrees to sell protection against losses on a tranche and the other side agrees to buy the protection. The tranche is not part of a synthetic CDO that someone has created but cash flows are calculated in the same way as if it were part of such a synthetic CDO.

9. Valuation of Synthetic CDO

10. Alternatives to the Standard Market Model
10-1. Heterogeneous Model
The standard market model is a homogeneous model in the sense that the time-to-default probability distributions are assumed to be the same for all companies and the copula correlations for any pair of companies are the same. The homogeneity assumption can be relaxed sh that the more general model is used.

10-2. Other Copulas
- one-factor Gaussian copulas: Student t copula, Clayton copula, Archimedean copula, Marshall-Olkin copula

10-3. Multiple Factors

10-4. Random Factor Loadings

10-5. Implied Copula Model

10-6. Dynamic Models