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
Pie Chart of Percent vs Type
Meatball Garlic 5.0% 2.3% Mushroom and Onion 9.2% Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball
Boxplot of Listing
900000 800000 700000 900000 800000
Scatterplot of Listing vs IncomePC
99
Probability Plot of Listing
Normal - 95% CI 900000
Mean StDev N AD P-Value 369687 156865 51 0.994 0.012
Scatterplot of Listing vs IncomePC
Histogram of Listing
14 12 80 10 100
Empirical CDF of Listing
Normal
Mean StDev N 369687 156865 51
Marginal Plot of Listing vs IncomePC
Pepperoni 21.8%
800000 700000 600000
95
700000 600000
90 80
e mc
2
Frequency
Listing
Listing
Percent
600000
70 60 50 40 30 20 10 5
8 6 4 2 0
Percent
Pepper and Onion 7.3%
60 40
1000000 800000
Listing
500000 400000 300000 200000 100000 15000
500000 400000 300000 200000 100000 15000
Listing
0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing
Sausage 5.8%
500000 400000 300000
600000 400000
20 0
Mushroom 16.2%
Plain 32.5%
200000 100000
200000 15000 20000 25000 IncomePC 30000
17500
20000
22500 25000 IncomePC
27500
30000
32500
1
0
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400000 600000 Listing
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22500 25000 IncomePC
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700000
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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
Meatball Garlic 5.0% 2.3% Mushroom and Onion 9.2% Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball
Boxplot of Listing
900000 800000 700000 900000 800000
Scatterplot of Listing vs IncomePC
99
Probability Plot of Listing
Normal - 95% CI 900000
Mean StDev N AD P-Value 369687 156865 51 0.994 0.012
Scatterplot of Listing vs IncomePC
Histogram of Listing
14 12 80 10 100
Empirical CDF of Listing
Normal
Mean StDev N 369687 156865 51
Pepperoni 21.8%
800000 700000 600000
95
700000 600000
90 80
e mc
2
Frequency
Listing
Listing
Percent
600000
70 60 50 40 30 20 10 5
8 6 4 2 0
Percent
Pepper and Onion 7.3%
60 40
1000000 800000
Listing
500000 400000 300000 200000 100000 15000
500000 400000 300000 200000 100000 15000
Listing
0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing
Sausage 5.8%
500000 400000 300000
600000 400000
20 0
Mushroom 16.2%
Plain 32.5%
200000 100000
200000 15000 20000 25000 IncomePC 30000
17500
20000
22500 25000 IncomePC
27500
30000
32500
1
0
200000
400000 600000 Listing
800000
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The Insurance Policy
Snidely Whiplash (SW) sells RoG an insurance policy against the risk that RB will default on the loan (bond)
Pie Chart of Percent vs Type
Meatball Garlic 5.0% 2.3% Mushroom and Onion 9.2% Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball
Boxplot of Listing
900000 800000 700000 900000 800000
Scatterplot of Listing vs IncomePC
99
Probability Plot of Listing
Normal - 95% CI 900000
Mean StDev N AD P-Value 369687 156865 51 0.994 0.012
Scatterplot of Listing vs IncomePC
Histogram of Listing
14 12 80 10 100
Empirical CDF of Listing
Normal
Mean StDev N 369687 156865 51
Marginal Plot of Listing vs IncomePC
Pepperoni 21.8%
800000 700000 600000
95
700000 600000
90 80
e mc
2
Frequency
Listing
Listing
Percent
600000
70 60 50 40 30 20 10 5
8 6 4 2 0
Percent
Pepper and Onion 7.3%
60 40
1000000 800000
Listing
500000 400000 300000 200000 100000 15000
500000 400000 300000 200000 100000 15000
Listing
0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing
Sausage 5.8%
500000 400000 300000
600000 400000
20 0
Mushroom 16.2%
Plain 32.5%
200000 100000
200000 15000 20000 25000 IncomePC 30000
17500
20000
22500 25000 IncomePC
27500
30000
32500
1
0
200000
400000 600000 Listing
800000
1000000
17500
20000
22500 25000 IncomePC
27500
30000
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200000
300000
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500000 600000 Listing
700000
800000
900000
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.
Pie Chart of Percent vs Type
Meatball Garlic 5.0% 2.3% Mushroom and Onion 9.2% Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball
Boxplot of Listing
900000 800000 700000 900000 800000
Scatterplot of Listing vs IncomePC
99
Probability Plot of Listing
Normal - 95% CI 900000
Mean StDev N AD P-Value 369687 156865 51 0.994 0.012
Scatterplot of Listing vs IncomePC
Histogram of Listing
14 12 80 10 100
Empirical CDF of Listing
Normal
Mean StDev N 369687 156865 51
Marginal Plot of Listing vs IncomePC
Pepperoni 21.8%
800000 700000 600000
95
700000 600000
90 80
e mc
2
Frequency
Listing
Listing
Percent
600000
70 60 50 40 30 20 10 5
8 6 4 2 0
Percent
Pepper and Onion 7.3%
60 40
1000000 800000
Listing
500000 400000 300000 200000 100000 15000
500000 400000 300000 200000 100000 15000
Listing
0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing
Sausage 5.8%
500000 400000 300000
600000 400000
20 0
Mushroom 16.2%
Plain 32.5%
200000 100000
200000 15000 20000 25000 IncomePC 30000
17500
20000
22500 25000 IncomePC
27500
30000
32500
1
0
200000
400000 600000 Listing
800000
1000000
17500
20000
22500 25000 IncomePC
27500
30000
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700000
800000
900000
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)
Scatterplot of Listing vs IncomePC
900000 800000
95 99
Pie Chart of Percent vs Type
Meatball Garlic 5.0% 2.3% Mushroom and Onion 9.2% Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball
Boxplot of Listing
900000 800000 700000
Probability Plot of Listing
Normal - 95% CI 900000
Mean StDev N AD P-Value 369687 156865 51 0.994 0.012
Scatterplot of Listing vs IncomePC
Histogram of Listing
14 12 80 10 100
Empirical CDF of Listing
Normal
Mean StDev N 369687 156865 51
Marginal Plot of Listing vs IncomePC
Pepperoni 21.8%
800000 700000 600000
700000 600000
90 80
e mc
2
Frequency
Listing
Listing
Percent
600000
70 60 50 40 30 20 10 5
8 6 4 2 0
Percent
Pepper and Onion 7.3%
60 40
1000000 800000
Listing
500000 400000 300000 200000 100000 15000
500000 400000 300000 200000 100000 15000
Listing
0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing
Sausage 5.8%
500000 400000 300000
600000 400000
20 0
Mushroom 16.2%
Plain 32.5%
200000 100000
200000 15000 20000 25000 IncomePC 30000
17500
20000
22500 25000 IncomePC
27500
30000
32500
1
0
200000
400000 600000 Listing
800000
1000000
17500
20000
22500 25000 IncomePC
27500
30000
32500
200000
300000
400000
500000 600000 Listing
700000
800000
900000
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.
Pie Chart of Percent vs Type
Meatball Garlic 5.0% 2.3% Mushroom and Onion 9.2% Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball
Boxplot of Listing
900000 800000 700000 900000 800000
Scatterplot of Listing vs IncomePC
99
Probability Plot of Listing
Normal - 95% CI 900000
Mean StDev N AD P-Value 369687 156865 51 0.994 0.012
Scatterplot of Listing vs IncomePC
Histogram of Listing
14 12 80 10 100
Empirical CDF of Listing
Normal
Mean StDev N 369687 156865 51
Marginal Plot of Listing vs IncomePC
Pepperoni 21.8%
800000 700000 600000
95
700000 600000
90 80
e mc
2
Frequency
Listing
Listing
Percent
600000
70 60 50 40 30 20 10 5
8 6 4 2 0
Percent
Pepper and Onion 7.3%
60 40
1000000 800000
Listing
500000 400000 300000 200000 100000 15000
500000 400000 300000 200000 100000 15000
Listing
0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing
Sausage 5.8%
500000 400000 300000
600000 400000
20 0
Mushroom 16.2%
Plain 32.5%
200000 100000
200000 15000 20000 25000 IncomePC 30000
17500
20000
22500 25000 IncomePC
27500
30000
32500
1
0
200000
400000 600000 Listing
800000
1000000
17500
20000
22500 25000 IncomePC
27500
30000
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5 Ways The Contract Ends
Time t0 Time t1
Time t2
Time t3
Time t4
Pie Chart of Percent vs Type
Meatball Garlic 5.0% 2.3% Mushroom and Onion 9.2% Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball
Boxplot of Listing
900000 800000 700000 900000 800000
Scatterplot of Listing vs IncomePC
99
Probability Plot of Listing
Normal - 95% CI 900000
Mean StDev N AD P-Value 369687 156865 51 0.994 0.012
Scatterplot of Listing vs IncomePC
Histogram of Listing
14 12 80 10 100
Empirical CDF of Listing
Normal
Mean StDev N 369687 156865 51
Marginal Plot of Listing vs IncomePC
Pepperoni 21.8%
800000 700000 600000
95
700000 600000
90 80
e mc
2
Frequency
Listing
Listing
Percent
600000
70 60 50 40 30 20 10 5
8 6 4 2 0
Percent
Pepper and Onion 7.3%
60 40
1000000 800000
Listing
500000 400000 300000 200000 100000 15000
500000 400000 300000 200000 100000 15000
Listing
0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing
Sausage 5.8%
500000 400000 300000
600000 400000
20 0
Mushroom 16.2%
Plain 32.5%
200000 100000
200000 15000 20000 25000 IncomePC 30000
17500
20000
22500 25000 IncomePC
27500
30000
32500
1
0
200000
400000 600000 Listing
800000
1000000
17500
20000
22500 25000 IncomePC
27500
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700000
800000
900000
Joint Probabilities – The Contract Ends with Default at Time T2
Prob(Default at T1) =P(D1)
Prob(Not Default at T1) =P(ND1)
Prob(Default at T2|ND1) =P(D2|ND1)
Prob(Not Default at T2|ND1) =P(ND1)
P(Default at T2 and Not Default at T1) = P(D2|ND1)P(ND1) = P1(1-P2)
Pie Chart of Percent vs Type
Meatball Garlic 5.0% 2.3% Mushroom and Onion 9.2% Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball
Boxplot of Listing
900000 800000 700000 900000 800000
Scatterplot of Listing vs IncomePC
99
Probability Plot of Listing
Normal - 95% CI 900000
Mean StDev N AD P-Value 369687 156865 51 0.994 0.012
Scatterplot of Listing vs IncomePC
Histogram of Listing
14 12 80 10 100
Empirical CDF of Listing
Normal
Mean StDev N 369687 156865 51
Marginal Plot of Listing vs IncomePC
Pepperoni 21.8%
800000 700000 600000
95
700000 600000
90 80
e mc
2
Frequency
Listing
Listing
Percent
600000
70 60 50 40 30 20 10 5
8 6 4 2 0
Percent
Pepper and Onion 7.3%
60 40
1000000 800000
Listing
500000 400000 300000 200000 100000 15000
500000 400000 300000 200000 100000 15000
Listing
0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing
Sausage 5.8%
500000 400000 300000
600000 400000
20 0
Mushroom 16.2%
Plain 32.5%
200000 100000
200000 15000 20000 25000 IncomePC 30000
17500
20000
22500 25000 IncomePC
27500
30000
32500
1
0
200000
400000 600000 Listing
800000
1000000
17500
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22500 25000 IncomePC
27500
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700000
800000
900000
Present Values of Cash Flows
Sum = Expected PDV of Premium Payments
Pie Chart of Percent vs Type
Meatball Garlic 5.0% 2.3% Mushroom and Onion 9.2% Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball
Sum to obtain Expected Present Discounted Value of Default Payment
Scatterplot of Listing vs IncomePC
900000
Boxplot of Listing
900000 800000 700000 900000 800000
Scatterplot of Listing vs IncomePC
99
Probability Plot of Listing
Normal - 95% CI
Mean StDev N AD P-Value 369687 156865 51 0.994 0.012
Histogram of Listing
14 12 80 10 100
Empirical CDF of Listing
Normal
Mean StDev N 369687 156865 51
Marginal Plot of Listing vs IncomePC
Pepperoni 21.8%
800000 700000 600000
95
700000 600000
90 80
e mc
2
Frequency
Listing
Listing
Percent
600000
70 60 50 40 30 20 10 5
8 6 4 2 0
Percent
Pepper and Onion 7.3%
60 40
1000000 800000
Listing
500000 400000 300000 200000 100000 15000
500000 400000 300000 200000 100000 15000
Listing
0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing
Sausage 5.8%
500000 400000 300000
600000 400000
20 0
Mushroom 16.2%
Plain 32.5%
200000 100000
200000 15000 20000 25000 IncomePC 30000
17500
20000
22500 25000 IncomePC
27500
30000
32500
1
0
200000
400000 600000 Listing
800000
1000000
17500
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22500 25000 IncomePC
27500
30000
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700000
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900000
Expected Present Value
Pie Chart of Percent vs Type
Meatball Garlic 5.0% 2.3% Mushroom and Onion 9.2% Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball
Boxplot of Listing
900000 800000 700000 900000 800000
Scatterplot of Listing vs IncomePC
99
Probability Plot of Listing
Normal - 95% CI 900000
Mean StDev N AD P-Value 369687 156865 51 0.994 0.012
Scatterplot of Listing vs IncomePC
Histogram of Listing
14 12 80 10 100
Empirical CDF of Listing
Normal
Mean StDev N 369687 156865 51
Marginal Plot of Listing vs IncomePC
Pepperoni 21.8%
800000 700000 600000
95
700000 600000
90 80
e mc
2
Frequency
Listing
Listing
Percent
600000
70 60 50 40 30 20 10 5
8 6 4 2 0
Percent
Pepper and Onion 7.3%
60 40
1000000 800000
Listing
500000 400000 300000 200000 100000 15000
500000 400000 300000 200000 100000 15000
Listing
0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing
Sausage 5.8%
500000 400000 300000
600000 400000
20 0
Mushroom 16.2%
Plain 32.5%
200000 100000
200000 15000 20000 25000 IncomePC 30000
17500
20000
22500 25000 IncomePC
27500
30000
32500
1
0
200000
400000 600000 Listing
800000
1000000
17500
20000
22500 25000 IncomePC
27500
30000
32500
200000
300000
400000
500000 600000 Listing
700000
800000
900000
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.
Pie Chart of Percent vs Type
Meatball Garlic 5.0% 2.3% Mushroom and Onion 9.2% Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball
Boxplot of Listing
900000 800000 700000 900000 800000
Scatterplot of Listing vs IncomePC
99
Probability Plot of Listing
Normal - 95% CI 900000
Mean StDev N AD P-Value 369687 156865 51 0.994 0.012
Scatterplot of Listing vs IncomePC
Histogram of Listing
14 12 80 10 100
Empirical CDF of Listing
Normal
Mean StDev N 369687 156865 51
Marginal Plot of Listing vs IncomePC
Pepperoni 21.8%
800000 700000 600000
95
700000 600000
90 80
e mc
2
Frequency
Listing
Listing
Percent
600000
70 60 50 40 30 20 10 5
8 6 4 2 0
Percent
Pepper and Onion 7.3%
60 40
1000000 800000
Listing
500000 400000 300000 200000 100000 15000
500000 400000 300000 200000 100000 15000
Listing
0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing
Sausage 5.8%
500000 400000 300000
600000 400000
20 0
Mushroom 16.2%
Plain 32.5%
200000 100000
200000 15000 20000 25000 IncomePC 30000
17500
20000
22500 25000 IncomePC
27500
30000
32500
1
0
200000
400000 600000 Listing
800000
1000000
17500
20000
22500 25000 IncomePC
27500
30000
32500
200000
300000
400000
500000 600000 Listing
700000
800000
900000
There is a Solution
PV 0 implies (1 p1)1 p1(1 p 2) 2 4(1 R ) p1 p 2(1 p3)3 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 )
Probability Plot of Listing
Normal - 95% CI
99
c
Pie Chart of Percent vs Type
Meatball Garlic 5.0% 2.3% Mushroom and Onion 9.2% Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball
Boxplot of Listing
900000 800000 700000 900000 800000
Scatterplot of Listing vs IncomePC
Scatterplot of Listing vs IncomePC
900000
Mean StDev N AD P-Value 369687 156865 51 0.994 0.012
Histogram of Listing
14 12 80 10 100
Empirical CDF of Listing
Normal
Mean StDev N 369687 156865 51
Marginal Plot of Listing vs IncomePC
Pepperoni 21.8%
800000 700000 600000
95
700000 600000
90 80
e mc
2
Frequency
Listing
Listing
Percent
600000
70 60 50 40 30 20 10 5
8 6 4 2 0
Percent
Pepper and Onion 7.3%
60 40
1000000 800000
Listing
500000 400000 300000 200000 100000 15000
500000 400000 300000 200000 100000 15000
Listing
0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing
Sausage 5.8%
500000 400000 300000
600000 400000
20 0
Mushroom 16.2%
Plain 32.5%
200000 100000
200000 15000 20000 25000 IncomePC 30000
17500
20000
22500 25000 IncomePC
27500
30000
32500
1
0
200000
400000 600000 Listing
800000
1000000
17500
20000
22500 25000 IncomePC
27500
30000
32500
200000
300000
400000
500000 600000 Listing
700000
800000
900000
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.
Scatterplot of Listing vs IncomePC
900000 800000
95 99
Pie Chart of Percent vs Type
Meatball Garlic 5.0% 2.3% Mushroom and Onion 9.2% Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball
Boxplot of Listing
900000 800000 700000
Probability Plot of Listing
Normal - 95% CI 900000
Mean StDev N AD P-Value 369687 156865 51 0.994 0.012
Scatterplot of Listing vs IncomePC
Histogram of Listing
14 12 80 10 100
Empirical CDF of Listing
Normal
Mean StDev N 369687 156865 51
Marginal Plot of Listing vs IncomePC
Pepperoni 21.8%
800000 700000 600000
700000 600000
90 80
e mc
2
Frequency
Listing
Listing
Percent
600000
70 60 50 40 30 20 10 5
8 6 4 2 0
Percent
Pepper and Onion 7.3%
60 40
1000000 800000
Listing
500000 400000 300000 200000 100000 15000
500000 400000 300000 200000 100000 15000
Listing
0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing
Sausage 5.8%
500000 400000 300000
600000 400000
20 0
Mushroom 16.2%
Plain 32.5%
200000 100000
200000 15000 20000 25000 IncomePC 30000
17500
20000
22500 25000 IncomePC
27500
30000
32500
1
0
200000
400000 600000 Listing
800000
1000000
17500
20000
22500 25000 IncomePC
27500
30000
32500
200000
300000
400000
500000 600000 Listing
700000
800000
900000
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
Pie Chart of Percent vs Type
Meatball Garlic 5.0% 2.3% Mushroom and Onion 9.2% Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball
Boxplot of Listing
900000 800000 700000 900000 800000
Scatterplot of Listing vs IncomePC
99
Probability Plot of Listing
Normal - 95% CI 900000
Mean StDev N AD P-Value 369687 156865 51 0.994 0.012
Scatterplot of Listing vs IncomePC
Histogram of Listing
14 12 80 10 100
Empirical CDF of Listing
Normal
Mean StDev N 369687 156865 51
Marginal Plot of Listing vs IncomePC
Pepperoni 21.8%
800000 700000 600000
95
700000 600000
90 80
e mc
2
Frequency
Listing
Listing
Percent
600000
70 60 50 40 30 20 10 5
8 6 4 2 0
Percent
Pepper and Onion 7.3%
60 40
1000000 800000
Listing
500000 400000 300000 200000 100000 15000
500000 400000 300000 200000 100000 15000
Listing
0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing
Sausage 5.8%
500000 400000 300000
600000 400000
20 0
Mushroom 16.2%
Plain 32.5%
200000 100000
200000 15000 20000 25000 IncomePC 30000
17500
20000
22500 25000 IncomePC
27500
30000
32500
1
0
200000
400000 600000 Listing
800000
1000000
17500
20000
22500 25000 IncomePC
27500
30000
32500
200000
300000
400000
500000 600000 Listing
700000
800000
900000
Pie Chart of Percent vs Type
Meatball Garlic 5.0% 2.3% Mushroom and Onion 9.2% Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball
Boxplot of Listing
900000 800000 700000 900000 800000
Scatterplot of Listing vs IncomePC
99
Probability Plot of Listing
Normal - 95% CI 900000
Mean StDev N AD P-Value 369687 156865 51 0.994 0.012
Scatterplot of Listing vs IncomePC
Histogram of Listing
14 12 80 10 100
Empirical CDF of Listing
Normal
Mean StDev N 369687 156865 51
Marginal Plot of Listing vs IncomePC
Pepperoni 21.8%
800000 700000 600000
95
700000 600000
90 80
e mc
2
Frequency
Listing
Listing
Percent
600000
70 60 50 40 30 20 10 5
8 6 4 2 0
Percent
Pepper and Onion 7.3%
60 40
1000000 800000
Listing
500000 400000 300000 200000 100000 15000
500000 400000 300000 200000 100000 15000
Listing
0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing
Sausage 5.8%
500000 400000 300000
600000 400000
20 0
Mushroom 16.2%
Plain 32.5%
200000 100000
200000 15000 20000 25000 IncomePC 30000
17500
20000
22500 25000 IncomePC
27500
30000
32500
1
0
200000
400000 600000 Listing
800000
1000000
17500
20000
22500 25000 IncomePC
27500
30000
32500
200000
300000
400000
500000 600000 Listing
700000
800000
900000
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.
Pie Chart of Percent vs Type
Meatball Garlic 5.0% 2.3% Mushroom and Onion 9.2% Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball
Boxplot of Listing
900000 800000 700000 900000 800000
Scatterplot of Listing vs IncomePC
99
Probability Plot of Listing
Normal - 95% CI 900000
Mean StDev N AD P-Value 369687 156865 51 0.994 0.012
Scatterplot of Listing vs IncomePC
Histogram of Listing
14 12 80 10 100
Empirical CDF of Listing
Normal
Mean StDev N 369687 156865 51
Marginal Plot of Listing vs IncomePC
Pepperoni 21.8%
800000 700000 600000
95
700000 600000
90 80
e mc
2
Frequency
Listing
Listing
Percent
600000
70 60 50 40 30 20 10 5
8 6 4 2 0
Percent
Pepper and Onion 7.3%
60 40
1000000 800000
Listing
500000 400000 300000 200000 100000 15000
500000 400000 300000 200000 100000 15000
Listing
0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing
Sausage 5.8%
500000 400000 300000
600000 400000
20 0
Mushroom 16.2%
Plain 32.5%
200000 100000
200000 15000 20000 25000 IncomePC 30000
17500
20000
22500 25000 IncomePC
27500
30000
32500
1
0
200000
400000 600000 Listing
800000
1000000
17500
20000
22500 25000 IncomePC
27500
30000
32500
200000
300000
400000
500000 600000 Listing
700000
800000
900000