12. NO Credit Event
CDS BUYER
BOND BUYER
NO payoff
CDS Spread
CDS SELLER
BOND ISSUER
13. 1
2
Physical Settlement
100 million = 100 million
Credit Event
Cash Settlement
• Auction to determine the mid-market value of
the cheapest deliverable bond
• If bond is worth $35 per $100 of its face value
• 65 million dollars
17. Speculation
1. They can buy CDS on bonds they don’t
own
2. They can sell CDS to others
Will Improve
Will default
=
Buy CDS
Sell
“ Naked Credit Default Swap ”
18. Risk
Counterparty risk –Taken by buyer
BANK
Risky
Seller Default
Counterparty risk
Corp.
Double Default
Risky
BANK
Corp.
Buyer loses its
protection against
default by the
reference entity
Buyer needs to
replace the defaulted
CDS at a higher cost
19. Risk
Counterparty risk
- taken by seller
Buyer Default
Seller can limit loss by hedging its exposure
- Unwinding the hedge transaction
- Selling a new CDS to a third party
40. Terms Definition: Default Probability
The likelihood that the
borrower will not be able
to make repayments
41. Terms Definition: Survival Probability
The likelihood that the
company will survive and
make payments on their
debt
42. Terms Definition: Recovery Rate
Amount recovered in
the event of a default
as a percent of the
face value
43. Assumption
•
•
•
•
•
•
Defaults happen at midyear every year
throughout life of the CDS
Buyer of a CDS make payment annually
Risk-free rate = 5% (continuous compounding)
Recovery rate = 40%
Time= 5 years
Probability of default= 2%
Defa
Defa
Def
Defa
Defa
44. Default Probabilities and Survival Probabilities
Marginal
probability of
default
Cumulative
probability of
survival
Time (years)
Default Probability
Survival Probability
1
0.0200
0.9800
2
0.0196
0.9604
0.9800x0.9800
3
0.0192
0.9412
0.9800x0.9604
4
0.0188
0.9224
0.9800x0.9412
5
0.0184
0.9039
0.9800x0.9224
Calculated by
multiplying
default
45. Valuation Concept
PV of
Payment
made by CDS
buyer
1
=
Payment
2
Accrual
payment
When
reference
firm does
When
reference
firm
3
PV of Payoff
made by CDS
seller
46. Step1. Calculation of the PV of Expected Payment
1
Time Probability of
(year)
Survival
1
2
3
4
5
Total
0.9800
0.9604
0.9412
0.9224
0.9039
2
1 X2
Expected
Payment
Discount
Factor
0.9800s
0.9604s
0.9412s
0.9224s
0.9039s
0.9512
0.9048
0.8607
0.8187
0.7788
PV of
Expected
Payment
0.9322s
0.8690s
0.8101s
0.7552s
0.7040s
4.0704s
Discount factor = e-rt
* S= annual
47. Step 2. Accrual payment made in the event of default
1
2
Time
(year)
Probability of
Default
Expected
Accrual
Payment
0.5
1.5
2.5
3.5
4.5
Total
0.0200
0.0196
0.0192
0.0188
0.0184
0.0100s
0.0098s
0.0096s
0.0094s
0.0092s
Remember
we assume
that the
defaults
Discount Factor
0.9753
0.9277
0.8825
0.8395
0.7985
Expected
Accrual
Payment =
Prob. Of
1
X
2
PV of
Expected
Accrual
Payment
0.0098s
0.0091s
0.0085s
0.0079s
0.0074s
0.0426s
48. Step 3. Calculation of PV of Expected Payoff
1
Time
0.5
1.5
2.5
3.5
4.5
Total
Probability Recovery
of Default
Rate
0.0200
0.0196
0.0192
0.0188
0.0184
0.4
0.4
0.4
0.4
0.4
2
Expected
Payoff
Discount
Factor
0.0120
0.0118
0.0115
0.0113
0.0111
0.9753
0.9277
0.8825
0.8395
0.7985
1
X
2
PV off
Expected
Payoff
0.0117
0.0109
0.0102
0.0095
0.0088
0.0511
Expected Payoff
= Prob. Of
Default x 0.6
0.6 comes from
49. Finding CDS spread
The mid-market CDS spread
for the 5 year deal should be
124 basis point !
Step 1
Step 2
Step 3
4.0704s + 0.0426s = 0.0511
s = 0.0124
Editor's Notes
When entering into a CDS, both the buyer and seller of credit protection take on counterparty riskThe buyer takes the risk that the seller may default. First case, if AAA-Bank and Risky Corp. default simultaneously or “double default,” the buyer loses its protection against default by the reference entity. If AAA-Bank defaults but Risky Corp. does not, the buyer might need to replace the defaulted CDS at a higher cost.
For the seller, they take the risk that the buyer may default on the contract, depriving the seller of the expected revenue stream. Therefore, a seller normally limits its risk by buying offsetting protection from another party, that is, it hedges its exposure. If the original buyer drops out, the seller squares its position by either unwinding the hedge transaction or by selling a new CDS to a third party. Depending on market conditions, they may be able to sell at a lower price than the original CDS and may therefore involve a loss to the seller.
As is true with other forms of over-the-counter derivative, CDS might involve liquidity risk. It is common that one or both parties to a CDS contract must post collateral. So, there can be margin calls requiring the posting of additional collateral. The required collateral is agreed on by the parties when the CDS is first issued. This margin amount may vary over the life of the CDS contract, if the market price of the CDS contract changes, or the credit of one of the parties changes. Many CDS contracts even require payment of an upfront fee.
Another kind of risk for the seller of credit default swaps is jump risk or jump-to-default risk.A seller of a CDS could be collecting monthly premiums with little expectation that the referenceentity may default. A default creates a sudden obligation on the protection sellers to pay millions, if not billions, of dollars to protection buyers. Therefore, if the seller does not set aside the money to pay to the buyer in case of the default, a huge crisis might follow.
