Default Correlations and Credit Default Swaps
Cara Herlihy
Mathematical Sciences Seminar: Monte Carlo Methods
May 2, 2011
Herlihy 2
The economic recession of 2006 came as a shock to people all over the world. Many
banks, private institutions and individuals not only lost exorbitant amounts of money but lost
confidence in the economy as well. When looking back on the recession there is not one, but
multiple factors that contributed to the downfall of the economy. Two financial concepts that
have been repeatedly criticized for having momentous effects on the recession are Default
Correlations and Credit Default Swaps. Both concepts were popular before the recession but
became more popular after because of the ways in which their practices were altered due to the
unforeseen circumstances of the recession.
Correlation is a technique that is used in statistics to demonstrate the strength of the
relationship between two variables. Default correlation pinpoints the relationship between two
variables defaulting within a portfolio. More specifically, default correlation measures whether
risky credit assets are more likely to default together or separately. In simpler terms, if you have
a portfolio with two assets (i.e. stocks or bonds), what is the chance that the probability of asset 1
defaulting has an effect on the probability of asset 2 defaulting? If there is a high chance that the
probability of the assets directly affects each other then there is a strong default correlation. If
not, then the assets are considered to have a low default correlation.
There are three types of default correlations that are relevant within a portfolio. Zero
correlation means that the outcome of one asset defaulting has no effect on the other asset
defaulting which shows that the companies are independent of each other. Positive default
correlation between two assets means that if one asset defaults then the other asset is directly
affected and will default as well. Negative default correlation between two assets means that if
one asset defaults, then the likelihood of the other defaulting will decrease (Pareek).
Herlihy 3
Default correlation are an important figure to look at, especially for investment
professionals. This is because default correlation is one of three factors in determining the credit
risk of a portfolio. Specifically, default correlation affects the risk-return profile of an investment
in risky credit assets (Lucas). With the specified correlation, investors are able to compare the
expected returns of an investment to the amount of risk undertaken to get the returns. It is a way
for the investment professionals to gage if the risk they are taking is worth the losses that might
ensue.
In order for investors to limit their losses many have started to practice the idea of
securitization. Securitization is a financial transaction in which assets are pooled and securities
representing interests in the pool are issued. By taking different securities and pooling them
together it creates an opportunity to sell them as interest bearing securities (Jobst). After the
securities are sold, the interest and payments are paid out to the purchasers of the securities
dependent upon the securities tranche.
One relatively new way that investors securitize their portfolios is by structuring them as
Collateralized debt obligations (CDO). A CDO is a security that is backed by a pool of bonds,
loans and other assets. Some examples of the types of securities that could be found in a CDO
are Asset-Backed Securities (ABS), Mortgage Backed Securities (MBS), and Real Estate
Mortgage Backed Securities (RMBS). CDO’s are divided into tranches, which are then paid out
in through a ‘cashflow waterfall’ (Lucas). Tranches are designed to group together a specific
class of bonds that have similar levels of risk. The senior tranches receive a higher rating from
credit rating agencies because they are generally safer investments. Similarly, the junior tranches
receive a lower rating from the credit rating agencies because they are riskier investments. A
cashflow waterfall is a payment process that determines which securities get paid out throughout
Herlihy 4
the portfolio and in which order. All immediate payments to the investor, including principal
and interest, must be paid to the senior tranches before payments can be made to the junior
tranches. If all payments are not made to the senior tranches then the payment to the junior
tranche investors will not happen (Royer). As a result of this payment process, the junior
tranches are higher risk and therefore result in higher return.
Collateralized debt obligations are important investment tools because they have the
opportunity to be diversified. Diversifying a portfolio reduces the investment risk because it
allows for the inclusions of a spread of investments with various levels of risk so that it is not
solely dependent on the outcome of one security (Jobst). The concept of diversifying is often
compared to the proverb ‘don’t put all of your eggs in one basket’. For instance, if you had a
dozen eggs and you put all of them in one basket and that basket falls then all of your eggs break.
However, if you separate your eggs into twelve different baskets and one of them happens to fall,
you are still left with eleven eggs which isn’t a complete loss.
Default correlations within a portfolio have an overall effect on the volatility and return
of the portfolio. If the default correlation is low, then the volatility of the portfolio will decrease.
This is because if the defaults of the assets are independent, the overall variation in the price over
time will be small. On the other hand, if the default correlation within a portfolio is high then the
volatility will increase because there is a greater chance that if one assets price changes, the
others will be affected and change as well (Lucas).
There are various factors that can cause a change in the rate of default correlation. One
major factor is the overall state of the economy. If the economy is doing poorly and people are
struggling to stay afloat, then they are more likely to default on the loans that they have. The
Herlihy 5
economy affects the entire country, so if one person is going to be affected there is a greater
chance that more people will be affected as well. Another factor that can cause an influx of
default correlations is the state of a particular region or industry. For instance, if a major power
plant is the employer of the majority of people in one town, then the town is very dependent on
the well being of the plant. If the power plant were to go out of business then the probability of
many people in the town defaulting on their loans would increase because they would not be
receiving an income. This would greatly increase the levels of default correlations for this area
because many people are being affected by the same factor. Yet another factor that could cause a
change in the level of default correlation would be if there was a direct relationship between
parties. For example, if there is a situation where A pays B for a loan each month but A defaults
on their loan to B, then B is more likely to default on a loan to C. This is because the income B
should have been collecting from A has ceased, and now B has no funds to pay C with. If there is
a web between parties then one party defaulting can have a detrimental effect throughout the rest
of the web.
Although the concept of default correlation can be applied to any instance in which a loan
is taken out, default correlations among subprime mortgages had an important role in the subprime mortgage. The sub-prime mortgage crisis started in 2006 when there was a rise in the
number of sub-prime mortgage delinquencies and foreclosures that effected banks and lending
institutions. In the years before the crisis, U.S. housing prices were increasing at a promising rate
which resulted in many people investing in houses. Banks became more lenient with their criteria
for loan qualifications which attracted borrowers that were previously unqualified. Many banks
offered Adjustable-Rate mortgages that lured borrowers into loans with extremely low interest
rates for a set period of time until the rate was adjusted at a later date. This encouraged
Herlihy 6
borrowers to assume difficult mortgages in the hopes that the prices of their houses would
continue to appreciate, and they could refinance at a later date (“Variable- Rate Mortgages”).
The crisis was initially set off by the bursting of the U.S. Housing bubble in 2006. As prices of
houses started to decrease, many of the interest rates on the loans were re-set higher and
refinancing for the borrowers became more difficult. This led to a high rate on delinquencies on
mortgages because the amounts that people were paying for their houses became more than the
actual values of their homes. Many people entered themselves into foreclosure because it was
better financial option than the one they found themselves in. Defaults on mortgage loans went
from being completely random, to being highly correlated because of the unforeseen
circumstances.
An example of how default correlations played a role in the financial crisis can be shown
through the effects of defaults on mortgages throughout one neighborhood. Assume there are
three houses on one street of a particular neighborhood. Owner 1 defaults on his mortgage
because he loses his job. As a result, his house goes into foreclosure and this in turn brings down
the values of the houses in his neighborhood. Living in an area with decreasing house prices,
Owner 2 feels the repercussions of Owner 1foreclosing. The price of his house depreciates and
he cannot afford his mortgage payments anymore, so it is in his best financial interest to
foreclose. In enters Owner 3. With both of his neighbors foreclosing, the neighborhood becomes
less desirable and the prices of Owner 3’s house declines. After refinancing, Owner 3’s house is
significantly less than what he anticipated it would be when he singed his adjustable- rate
mortgage. As a result he cannot pay the new payment for his mortgage and he defaults on his
mortgage loan.
Herlihy 7
For my project I did two simulations in R-Code to ill illustrate default correlation. The
first simulation I did showed the number of defaults within a portfolio having independent
assets. For this simulation a binomial distribution was used because there were only two
outcomes possible: whether the loan is being defaulted on or not. I set the parameters for the
number of bonds to the value n, and the number of default probability to pavg. The binomial
distribution section of the R Code is shown through Figure 1. The second simulation I
constructed illustrated the number of defaults within a portfolio when default correlations
between assets were correlated. A beta distribution is used because we are interested in the
events that take place within a set interval (0,1) (Johnson and Beverlin). The minimum outcome
would results from zero of the loans defaulting, and the maximum outcome would results from
all of the loans defaulting. In this case, the beta distribution is used to show the variety of the
defaults with an appointed value of pavg. For the correlated simulation, the result for the beta
distribution placed as a variable in the binomial distribution from the independent version. The
value of C, which can be any number that is greater than zero, is used as a constant to illustrate
the spread of data. The beta distribution section of the R Code is shown through Figure 2.
The graphs that were a result of my simulations clearly illustrate the differences between
the frequencies of defaults within a portfolio for default independent examples and default
dependent examples. By comparing graphs of C=1 to C=10, we can see how the value of the
constant C effects the number of defaults (Figure 2.1).With a smaller number for C we can see
that there is a greater variation in the spread of data for the correlated versions by observing the
sporadic placements of the dots that signify number of defaults. When the value of C is increased
to 10, we can see that the spread of data narrows and data becomes more focused which
illustrates a dependent relationship.
Herlihy 8
Another financial concept that is highly dependent on default correlations as well as
highly critiqued for contributing the financial crisis is the utilization of Credit Default Swaps.
Credit Default Swaps were designed to transfer the credit exposure of fixed income products
between parties (Mauer, Zhang, and Zhao). In other words, it is a type of ‘insurance’
arrangement in which the buyers pays a premium at periodic intervals in exchange for a
conditional payment from the issuer in the event of a default. Investors can purchase Credit
Default Swaps if they think that the risk of a company defaulting is about to increase. Investors
also buy Credit Default Swaps if the risk of the company defaulting is low but they wish to
eliminate all possible risks. Buying a Credit Default Swap is a matter of preference and is not
mandatory regardless of the level of default probability of an asset.
Credit Default Swaps involves two parties that are directly affected by the risk of a third
party (the reference entity) defaulting on its loan. The buyer of the Credit Default Swap agrees to
pay a fixed “premium” to the seller of the contract. In return, the seller of the Credit Default
Swap agrees to buy the specified bond (or loan) from the buyer at par if a ‘credit event’ occurs.
In the instance of a ‘credit event’ the seller pays the buyer an amount equal to the amount they
lost on their bond position. The premium that the buyer pays is calculated as the percentage of
face value of the bond, and is paid at a periodic interval throughout the contract. It is important to
note that the issuer is only required to pay the full amount to the buyer in the occurrence of a
credit event, but not in the instances when the bond prices fluctuate (Stulz).
Credit Default Swaps are often referred to as types of insurance. Although the two have
similarities they also have differences which should be duly noted. The first major difference that
the two have is the actual holding of the product that they wish to ‘insure’. In the case of
insurance, you need direct economic exposure in order to purchase the insurance. For instance, if
Herlihy 9
you want fire insurance on your house you must actually own a house in which you wish to buy
the insurance on. In the case of a Credit Default Swap, you do not need to hold or own the bonds
in order to buy a Credit Default Swap on them. As long as you pay a premium to the issuer they
will cover you in the occurrence of a credit event. Another notable difference between the two is
the fact that Credit Default Swaps are traded and insurance policies are not. Credit Default
Swaps are constantly traded to shift the levels of risk that issuers take on and by doing so create a
profit for people trading them. There is no legal form of trading insurance policies.
Seeing that the payment from the issuer is directly dependant on the ‘credit event’ of the
reference entity, it is important to clearly define specific criteria for what constitutes a credit
event. Bankruptcy, failure to pay, and restructuring are three events that constitute a credit event.
Restructuring is when a company changes its payment schedule on bonds. It is categorized as a
‘credit event’ because it usually puts the bondholders at a disadvantage and therefore can cause
the rate of their defaults to fluctuate (Restructuring Bond Debt in the Global Marketplace). If the
reference entity in question is more likely to default, then the issuer of protection will charge a
higher premium rate than that of a less risky asset. The risk of the likelihood of default is shown
through the bond tranches and ratings of the bonds.
The value of a Credit Default Swap is open for fluctuation based on the probability of
the default of the loans. At the time of purchase, the value for the protection buyer is zero. If the
probability of default becomes less likely, the value of the Credit Default Swap for the buyer will
decrease. This is because the buyer is essentially losing money because they are still required to
make the premium payments even though the investment is less risky. If the probability of
default increases the value of the Credit Default Swap for the buyer will increase. This is because
if the buyer had not opted to purchase the Credit Default Swap and a credit event did occur, they
Herlihy 10
would have lost a lot of money on their investment. As the risk of the rate of default increases,
the premiums that the buyer is paying the issuer are well spent.
Credit Default Swaps are an attractive option not only to reduce the risk of an investment
but to use for an advantage on speculation within the market as well. Buyers of a Credit Default
Swap benefit by receiving protection on their loans. They are no longer plagued with worry
about the probability of default fluctuating because they know that they will receive full payment
regardless. Sellers benefit through the income that is acquired in the occasion where Credit
Default Swaps are purchased but the third party never defaults. In these instances the issuer is
collecting the premiums but they have no obligation to make a payment at the end of the deal.
Credit Default Swaps are also used by investors to speculate credit and hedge bond positions in
order to make a profit.
Credit Default Swaps are more commonly known for their negative implications than their
positive ones. The term Credit Default Swap tends to go hand in hand with the term recession
and is claimed as being ‘Wall Street’s Worst Invention’ (Gilani). As the result of placing the risk
on the issuer of the Credit Default Swap, the lender of the loan has less incentive to monitor the
loan that they approved. By shifting their risk, they can keep rewarding loans to people who have
poor credentials. In addition, the shifting of risk lead to a false sense of safety among investors.
For instance, when then default correlation is low and the issuer has to cover insurance for 1,000
loans if one defaults, it isn’t a big deal. However, people didn’t think about the implications if
the default correlation increased. If the issuer covered the same 1,000 loans but this time they
had a high default correlation, then they were taking on a large amount of risk. This could end up
being a monumental disaster for the issuer if many of the reference entities within the loans
default and the issuers have to make many payments.
Herlihy 11
A fair Credit Default Swap premium is set to equate the present value of all premium
payments to the present value of the expected default loss (Wu). The pricing of each Credit
Default Swap is based on the research done by the issuer which focuses on specific information
about the reference entity. A deciding factor for the pricing of a Credit Default Swap is also
based on if it is a single name contract or a multi-name contract. In the case of single name
contracts, the occurrence of a default on a debt will have a direct outcome. Seeing that it is only
one entity either they will be able to pay their loan or not. In the event of a multi-name contract,
there is more than one entity which does not lead to a direct outcome (Desrosiers). This is
because some people may default on their loans while others may not, so the debt will continue
making payments. As a result, the Credit Default Swaps are calculated differently based on their
varying levels of entities.
When looking at the effect that Credit Default Swaps had on the sub-prime mortgage
crisis it is helpful to look at the ABX index. The ABX is an index of a series of Credit Default
Swaps based on 20 bonds that consist of subprime mortgages. The index started in 2006 and was
issued my Markit, a financial services company. Each index is released every six months and
references 20 new subprime mortgage backed securities that took place prior to the 6 months in
the index (Lucas). The index vintage contains individual sub-indices with tranches AAA, AA, A,
BBB, BBB-. Each vintage references exposure to the same underlying 20 sub-prime mortgages.
The criteria in order for the mortgage backed securities to be included in the index is strict in
order to make the index as accurate as possible. The mortgage backed securities have to have a
minimum of $500 million in deal size at the issuance. In addition, there is a limited number of
deals within the mortgage backed securities that can be issued with the same originator. And
lastly, the underlying obligation must be rated by both Standard and Poor’s and Moody’s. The
Herlihy 12
index is interesting and important to investors because it reflects the price at which the Credit
Default Swap on the names of the securities are trading but does not represent the actual value of
the names.
The ABX index is used on Wall Street as a benchmark for the performance of the
subprime mortgages and is seen as a focal point for trading in the U.S. sub-prime debt markets.
A decline in the ABX shows investor belief that subprime mortgage holders will suffer financial
losses. An increase in the ABX index shows investor opinion for subprime mortgage holdings to
perform better as investments (“ABX Marks US Subprime Mortgage Inventory at Approx. 65 Cents on
the Dollar”). By using these indices it gives investors the ability to hedge risks on subprime
mortgages.
Similar to Credit Default Swaps, the ABX index is traded as well. Indices are traded
based on price terms with a predetermined fixed-spread. Prices are quotes as a percent of par for
each individual index of a given vintage. If the trade occurs at par, then the transaction is similar
to the transaction of the Credit Default Swap and the buyer of the protection pays the issuer a
fixed spread. However, if the trade occurs at a time when the price is not equal to par then
depending on the price, one of the parties must make an upfront payment. In the event where the
price is at a premium to par, then the seller of the swap must pay the buyer. In the instance where
the price is discounted, then the buyer of the protection must pay the seller (“ABX Follow-up”).
The ABX pricing is a window that reflects the interest of investors to buy or sell defaults based
on their views of the sub-prime mortgages. Looking at the ABX price helps investors’ project
cash flow models to project payment information about the securities like delinquencies, defaults
and losses.
Herlihy 13
The ABX prices saw a steep decline after the housing bubble burst in 2006. This was a
result of the developing sub-prime mortgage crisis that deteriorated the prices of homes across
the nation. For the 2006-1 index, the prices were slightly higher because securities included for
this index were from the last six months of 2005 when housing prices were still appreciating
(Figure 3). Correlation patterns of these prices and their changes over time offer insight into how
the market perceives riskiness of the different ABX tranches. After the bubble burst and default
correlations increased, confidence in the economy specifically in the sub-prime mortgage
department decreased. Delinquency rates and a downgrade in the ratings on the securities are
found to have a negative effect on the sub-prime mortgage pricing. (Figure 4).
In terms of buying a Credit Default Swap for bonds using the ABX index, you must
know the coupon, the price, and the factor of the security. The coupon is the annual payment as a
percent of the amount being insured at the beginning of each year. The price is the current index
value which represents an additional premium price above the coupon percentage. The factor is
the portion of principal currently outstanding which is initially 1 ("Pricing ABX Index for
Newbies"). In order to buy the ‘insurance’ on the day when the index comes out, you would
only pay: coupon price x amount being insured x factor of 1 (because the price index is always
100 for the day). However, if you decide to buy a Credit Default Swap at a later date you will
have to pay a different price for protection because the price index fluctuates (Shenn). Seeing
that the ABX index was first published in 2006, we have seen the prices for protection increase
dramatically as a factor of time. This is because of the high rates of delinquencies on sub-prime
mortgage backed securities after the housing bubble burst. As of this point in time, we only have
evidence of prices increasing as a function of time but this will not always be the case. When the
recession ends and investors become more confident in the economy and start to re-invest in sub-
Herlihy 14
prime mortgages, the price as a function of time is likely to decrease because there will be less
delinquencies and defaults on these types of loans.
For the second simulation of my project in R I elaborated on my previous code to create a
rate that an issuer of a Credit Default Swap would charge a buyer. In order to do this, I took the
number of defaults from my previous code and sorted them (Figure 5). By doing this it gives a
better idea of how greatly the number of defaults varies between the independent and correlated
versions. These groupings clearly show the extreme levels of defaults that occur when the default
correlation is high (Figure 6).
I then proceeded to take the 99th percentile for the number of defaults for both the
independent and correlated versions. After getting these results, I created a rate for a premium
based on the percentile of defaults (Figure 7). I calculated these rates through the equation:
(n*rate)-d99*1 ≥ 0 which simplifies to: rate ≥ (d99/n) . This equation illustrates the rate that the
issuer would need to charge in order to protect himself against a maximum loss of 1 %.
When looking at the rate calculated through R, the rate I found most interesting and
different from other rates was the 95th percentile rate for correlated defaults. In these simulations,
the rates of the default correlated versions were much lower when compared to the 99th and
99.5th percentiles. When examining why, I believe I found the solution through looking at the
data from the sort command. For the correlated versions, we often had a large number of runs
with zero defaults before we resulted in a small number of runs that showed high levels of
defaults resulting in right skewed data. Because of these results, only the tail end of these graphs
would give us the data needed in order to charge an accurate rate for Credit Default Swaps with
correlated defaults. However, the 95th percentile runs the risk of having data that does not show
Herlihy 15
high default correlation. As a result, the 95th percentile (which allows a 5 % loss) is clearly too
risky for an issuer dealing with high default correlations to use.
Knowledge of default correlations on reference entities is necessary information in
evaluating the price of a credit default swap. Without the knowledge of the impact on what a
high default correlation can do to a portfolio, issuers of Credit Default Swaps would be unable to
gage an appropriate rate to charge in order to make a profit. Before the recession, the relationship
between default correlations and Credit Default Swaps slipped under the radar because the
economy was good and the relationship between the two was causing immediate issues.
However, after the recession hit the importance of both of these concepts and their relationship to
each other have been extensively studied and attributed to the loss of billions of dollars.
Herlihy 16
numdef<-rbinom(100,n,pavg)
Figure 1
pact<-rbeta(1,c*pavg,c*(1-pavg))
numdef2[i]<-rbinom(1,n,pact)}
Figure 2
C=1
C=10
Figure 2.1
Herlihy 17
Figure 3: The ABX: How Do the Markets Price Subprime Mortgage Risk? (Fender
& Schneider).
Figure 4: The pricing of subprime mortgage risk in good times and bad: evidence from the
ABX.HE indices (Fender & Schneider).
Herlihy 18
numdef<-sort(numdef)
numdef2<-sort(numdef2)
numdef
numdef2
Figure 5
[1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[40] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3
[79] 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 5 5 6 6 6 6
[1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[27] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[53] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[79] 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 5 13 22 29 31 60 63
Figure 6
d99<-numdef[.99*nruns]
d99
d992<-numdef2[.99*nruns]
d992
rate1=d99/n
rate2=d992/n
rate1
rate2
Figure 7
Herlihy 19
Works Cited
"ABX Follow-up." Accrued Interest. 21 Feb. 2007. Web. 10 Apr. 2011.
<http://accruedint.blogspot.com/2007/02/abx-follow-up.html>.
"ABX Marks US Subprime Mortgage Inventory At Approx. 65 Cents On The Dollar." HOUSING
DERIVATIVES. Applications and Economics for the U.S. Housing Market, 1 Mar. 2008. Web.
15 Apr. 2011. <http://housingderivatives.typepad.com/housing_derivatives/2008/03/abx-marksus-su.html>.
Desrosiers, Mary Elizabeth. Prices of Credit Default Swaps and the Term Structure of Credit Risk. A
Professional Master's Project. WORCESTER POLYTECHNIC INSTITUTE, May 2007. Web.
18 Apr. 2011. <http://www.wpi.edu/Pubs/ETD/Available/etd-050107-220449/unrestricted/CDSDefault_Probability.pdf>.
Fender, Ingo, and Martin Schneider. "The ABX: How Do the Markets Price Subprime Mortgage
Risk." Bank for International Settlements Quarterly Review (2008). Print.
Gilani, Shah. "The Real Reason for the Global Financial Crisis…the Story No One's Talking
About." Money Morning. Web. 18 Sept. 2008. <http://moneymorning.com/2008/09/18/creditdefault-swaps/>.
Jobst, Andreas. "What Is Securitization?" Finance and Development, Feb. 2008. Web. 01 Apr. 2011.
Johnson, Paul, and Matt Beverlin. Beta Distribution. Beta Distribution. Paul Johnson, University of
Kansas, 11 Mar. 2006. Web. 30 Mar. 2011.
<http://pj.freefaculty.org/stat/Distributions/Beta.pdf>.
Lucas, Douglas. CDO Handbook. Publication. J.P. Morgan Securities, Global Structured Finance
Research, 29 May 2001. Web. 22 Apr. 2011.
<http://www.math.ust.hk/~maykwok/courses/MAFS521_07/JPMorganCDOHandbook.pdf>.
Lucas, Douglas. Default Correlation: From Definition to Proposed Solutions. Rep. UBS CDO Research,
11 Aug. 2004. Web. 12 Apr. 2011.
<http://www.defaultrisk.com/_pdf6j4/Default_Correlation_From_Dfnt_2_Prpsd_Sltns.pdf>.
Herlihy 20
Mauer, David, Harold Zhang, and Feng Zhao. Subprime Mortgage Defaults and Credit Default Swaps.
University of Texas at Dallas, May 2010. Web. 14 Apr. 2011.
<http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1615123#>.
Pareek, Mukul. "Default Correlations." Riskprep - Risk Education. RiskPrep, 30 June 2010. Web. 11
Apr. 2011. <http://www.riskprep.com/all-tutorials/37-exam-3/114-default-correlations>.
"Pricing ABX Index for Newbies." Quant Network - Education Resource from the Financial Capital. 2
June 2010. Web. Mar.-Apr. 2011. <http://www.quantnet.com/pricing-abx-index/>.
Restructuring Bond Debt in the Global Marketplace. Publication. Gibson, Dunn & Crucher LLP., 2004.
Web. 30 Apr. 2011.
<http://media.gibsondunn.com/fstore/documents/pubs/Restructuring_Bond_Debt.pdf>.
Royer, Mattieu. Collateralized Debt Obligations- an Overview. Rep. The Professional Risk Managers'
International Assosciation. Web. 11 Apr. 2011.
<http://www.prmia.org/Chapter_Pages/Data/NewYork/Royer_11_30_04.PDF>.
Shenn, Jody. "Subprime Mortgage Bond Derivatives Fall After NovaStar's Loss." Bloomberg - Business
& Financial News, Breaking News Headlines. Bloomberf, 21 Feb. 2007. Web. 18 Apr. 2011.
<http://www.bloomberg.com/apps/news?pid=newsarchive>.
Stultz, Renee. "Credit Default Swaps and the Credit Crisis." Journal of Economic Perspectives 2010th
ser. 24.1 (2010): 73-92. Print.
"Subprime Mortgage Crisis." Subprime Mortgage Crisis. 2010. Web. 1 Apr. 2011.
<http://www.stat.unc.edu/faculty/cji/fys/2010/subprime-mortgage.pdf>.
"Variable-Rate Mortgage." Wikipedia, the Free Encyclopedia. 15 Apr. 2011. Web. 01 May 2011.
<http://en.wikipedia.org/wiki/Variable-rate_mortgage>.
Wu, Liuren. A Primer on Credit Default Swaps. Baruch College and Bloomberg LP, 9 July 2008. Web.
13 Apr. 2011. <http://faculty.baruch.cuny.edu/lwu/papers/CDS_ov.pdf>.