Credit Default Swaps
Can someone explain to Brian
Williams what a CDS is?
An insurance policy taken out by a
buyer of a bond against the risk of
default by a bond seller.
The ticking bomb in the financial
markets
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
Category 900000 900000
Meatball 900000 14
e mc
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
Mushroom and Onion
9.2%
2.3%
Pepperoni
21.8%
Plain
Mushroom
Sausage
800000 800000
95
StDev
N
156865
51
800000 2 12
StDev
N
156865
51
AD 0.994 80
Pepper and Onion 700000 90 700000
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50 40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000
Essentially How it Works
Risky Business (RB) borrows $10,000,000 from Rock of
Gilbraltar (RoG). (RB Sells RoG a $10,000,000 bond.)
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
Category 900000 900000
Meatball 900000 14
e mc
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
Mushroom and Onion
9.2%
2.3%
Pepperoni
21.8%
Plain
Mushroom
Sausage
800000 800000
95
StDev
N
156865
51
800000 2 12
StDev
N
156865
51
AD 0.994 80
Pepper and Onion 700000 90 700000
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50 40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000
The Insurance Policy
Snidely Whiplash (SW) sells RoG an insurance
policy against the risk that RB will default on
the loan (bond)
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
Category 900000 900000
Meatball 900000 14
e mc
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
Mushroom and Onion
9.2%
2.3%
Pepperoni
21.8%
Plain
Mushroom
Sausage
800000 800000
95
StDev
N
156865
51
800000 2 12
StDev
N
156865
51
AD 0.994 80
Pepper and Onion 700000 90 700000
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50 40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000
http://en.wikipedia.org/wiki/Credit_default_swap
It’s Simple, Really…
Sellers of CDS contracts will give a par quote for a given
reference entity, seniority, maturity and restructuring e.g. a seller
of CDS contracts may quote the premium on a 5 year CDS
contract on Ford Motor Company senior debt with modified
restructuring as 100 basis points. The par premium is calculated
so that the contract has zero present value on the effective date.
This is because the expected value of protection payments is
exactly equal and opposite to the expected value of the fee
payments. The most important factor affecting the cost of
protection provided by a CDS is the credit quality (often proxied
by the credit rating of the reference obligation. Lower credit
ratings imply a greater risk that the reference entity will default on
its payments and therefore the cost of protection will be higher.
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
Category 900000 900000
Meatball 900000 14
e mc
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
Mushroom and Onion
9.2%
2.3%
Pepperoni
21.8%
Plain
Mushroom
Sausage
800000 800000
95
StDev
N
156865
51
800000 2 12
StDev
N
156865
51
AD 0.994 80
Pepper and Onion 700000 90 700000
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50 40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000
So (for Example), Here’s the
Deal
One year term.
Par Premium is c% (e.g., .02 or 2%)
Notional value is N (e.g., $10,000,000)
Premiums paid quarterly at times t1, t2, t3,
t4. Default, if it occurs, happens at one of
these times.
Quarterly premium payment = Nc/4 paid at
the end of the quarter. (Nc/4=$50,000)
Recovery rate is R (e.g., .50 or 50%). If RB
defaults, SW pays RoG N(1-R)
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
Category 900000 900000
Meatball 900000 14
e mc
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
Mushroom and Onion
9.2%
2.3%
Pepperoni
21.8%
Plain
Mushroom
Sausage
800000 800000
95
StDev
N
156865
51
800000 2 12
StDev
N
156865
51
AD 0.994 80
Pepper and Onion 700000 90 700000
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50 40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000
What’s Needed for SW and
RoG to Agree on a Deal
Probabilities of no default looking
ahead from time 0 are P1, P2, P3, P4.
These depend on the credit rating of
RB.
Discount rates for computing present
discounted values of cash flows to be
received 1, 2, 3, and 4 periods in the
future, δ1, δ2, δ3, δ4.
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
Category 900000 900000
Meatball 900000 14
e mc
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
Mushroom and Onion
9.2%
2.3%
Pepperoni
21.8%
Plain
Mushroom
Sausage
800000 800000
95
StDev
N
156865
51
800000 2 12
StDev
N
156865
51
AD 0.994 80
Pepper and Onion 700000 90 700000
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50 40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000
5 Ways The Contract Ends
Time t0
Time t1
Time t2
Time t3
Time t4
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
Category 900000 900000
Meatball 900000 14
e mc
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
Mushroom and Onion
9.2%
2.3%
Pepperoni
21.8%
Plain
Mushroom
Sausage
800000 800000
95
StDev
N
156865
51
800000 2 12
StDev
N
156865
51
AD 0.994 80
Pepper and Onion 700000 90 700000
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50 40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000
Joint Probabilities – The
Contract Ends with Default at
Time T2
Prob(Default at T1)
Prob(Not Default at T1)
=P(D1)
=P(ND1)
Prob(Default at T2|ND1) Prob(Not Default at
=P(D2|ND1) T2|ND1) =P(ND1)
P(Default at T2 and Not Default at T1) = P(D2|ND1)P(ND1) = P1(1-P2)
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
Category 900000 900000
Meatball 900000 14
e mc
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
Mushroom and Onion
9.2%
2.3%
Pepperoni
21.8%
Plain
Mushroom
Sausage
800000 800000
95
StDev
N
156865
51
800000 2 12
StDev
N
156865
51
AD 0.994 80
Pepper and Onion 700000 90 700000
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50 40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000
Present Values of Cash Flows
Sum = Expected PDV of Sum to obtain Expected Present
Premium Payments Discounted Value of Default Payment
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
Category 900000 900000
Meatball 900000 14
e mc
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
Mushroom and Onion
9.2%
2.3%
Pepperoni
21.8%
Plain
Mushroom
Sausage
800000 800000
95
StDev
N
156865
51
800000 2 12
StDev
N
156865
51
AD 0.994 80
Pepper and Onion 700000 90 700000
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50 40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000
Expected Present Value
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
Category 900000 900000
Meatball 900000 14
e mc
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
Mushroom and Onion
9.2%
2.3%
Pepperoni
21.8%
Plain
Mushroom
Sausage
800000 800000
95
StDev
N
156865
51
800000 2 12
StDev
N
156865
51
AD 0.994 80
Pepper and Onion 700000 90 700000
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50 40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000
Setting the Price
N,
The probabilities p1, p2, p3, p4,
The discount rates, δ1, δ2, δ3, δ4
The recovery rate, R
All known.
Set PV = 0.
The only unknown is c, which is the price.
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
Category 900000 900000
Meatball 900000 14
e mc
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
Mushroom and Onion
9.2%
2.3%
Pepperoni
21.8%
Plain
Mushroom
Sausage
800000 800000
95
StDev
N
156865
51
800000 2 12
StDev
N
156865
51
AD 0.994 80
Pepper and Onion 700000 90 700000
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50 40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000
There is a Solution
PV 0 implies
(1 p1)1
p1(1 p 2)
4(1 R )
2
p1 p 2(1 p3)3
c p1 p 2 p3(1 p 4)4
p1(1 p 2)1
p1 p 2(1 p3)( )
1 2
p1 p 2 p3(1 p 4)(1 2 3 )
p1 p 2 p3 p 4(1 2 3 4 )
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
Category 900000 900000
Meatball 900000 14
e mc
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
Mushroom and Onion
9.2%
2.3%
Pepperoni
21.8%
Plain
Mushroom
Sausage
800000 800000
95
StDev
N
156865
51
800000 2 12
StDev
N
156865
51
AD 0.994 80
Pepper and Onion 700000 90 700000
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50 40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000
So What’s the Big Deal?
Snidely Whiplash is an insurance company
He need not have any reserves to insure
that he can actually pay off if the borrower
really does default
There is no regulation over the forms of
these agreements.
There is no regulation and no agreement on
what constitutes a “credit event.”
So what? These are grownup willing buyers
and sellers who know what they are doing.
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
Category 900000 900000
Meatball 900000 14
e mc
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
Mushroom and Onion
9.2%
2.3%
Pepperoni
21.8%
Plain
Mushroom
Sausage
800000 800000
95
StDev
N
156865
51
800000 2 12
StDev
N
156865
51
AD 0.994 80
Pepper and Onion 700000 90 700000
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50 40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000
Why Do “We” Care?
There are about $60 trillion in existing CDS contracts, up from
less than $30T last year, up from about $13T in December
2005. Quadrupled in two years.
The pool of CDSs exploded as the underlying mortgage
backed securities began to look unpleasant (toxic).
The pool of underlying bonds grew far far less.
The underlying bonds that are the subject of these “bets” add
up to about $6 trillion.
Thus, essentially, $54T are side bets
Noone really believed (until last week) that all (or even some)
of these bonds would fail at once
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
Category 900000 900000
Meatball 900000 14
e mc
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
Mushroom and Onion
9.2%
2.3%
Pepperoni
21.8%
Plain
Mushroom
Sausage
800000 800000
95
StDev
N
156865
51
800000 2 12
StDev
N
156865
51
AD 0.994 80
Pepper and Onion 700000 90 700000
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50 40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
Category 900000 900000
Meatball 900000 14
e mc
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
Mushroom and Onion
9.2%
2.3%
Pepperoni
21.8%
Plain
Mushroom
Sausage
800000 800000
95
StDev
N
156865
51
800000 2 12
StDev
N
156865
51
AD 0.994 80
Pepper and Onion 700000 90 700000
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50 40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000
How Does This Relate to
This Course?
The PDV is an expected value
The price setting mechanism is a fair game – set the
expected PDV to zero. This looks exactly like our
warranty calculation.
The default probabilities are conditioned on
borrower specific information (just like Fair Isaac)
The probabilities are based on a probability model
that is essentially the same as our light bulb model.
The paths to termination of the CDS look like our
analysis of litigation risk in using conditional and
marginal probabilities.
Marginal Plot of Listing vs IncomePC
Pie Chart of Percent vs Type Boxplot of Listing Scatterplot of Listing vs IncomePC Probability Plot of Listing Scatterplot of Listing vs IncomePC Histogram of Listing Empirical CDF of Listing
Normal - 95% CI Normal
Category 900000 900000
Meatball 900000 14
e mc
Pepperoni 99 Mean 369687
Garlic 5.0% Mean 369687 100
Mushroom and Onion
9.2%
2.3%
Pepperoni
21.8%
Plain
Mushroom
Sausage
800000 800000
95
StDev
N
156865
51
800000 2 12
StDev
N
156865
51
AD 0.994 80
Pepper and Onion 700000 90 700000
700000 P-Value 0.012
Mushroom and Onion 10
Garlic 80 1000000
600000 600000 60
Frequency
Pepper and Onion
Percent
Meatball 70
600000
Listing
Listing
7.3% 8
Percent
60 800000
500000 500000
Listing
50 40
Sausage 500000 40 6
Listing
5.8% 400000 30 400000 600000
400000 20 20
300000 300000 4
10 400000
300000 200000 5 200000 2 0
Mushroom Plain
16.2%
200000
32.5%
200000 0 00 00 00 00 00 00 00 00 00
100000 100000
1 0 00 00 00 00 00 00 00 00 00
15000 17500 20000 22500 25000 27500 30000 32500 0 200000 400000 600000 800000 1000000 15000 17500 20000 22500 25000 27500 30000 32500 200000 300000 400000 500000 600000 700000 800000 900000 10 20 30 40 50 60 70 80 90 15000 20000 25000 30000
IncomePC Listing IncomePC Listing Listing IncomePC
100000