about me
art
biz
Chess
corrections
economics
EconoSchool
Finance
friends
fun
game theory
games
geo
mathstat
misc
NatScience
... more
Profil
Logout
Subscribe Weblog

 
This post explains the Vasicek/Merton single factor model which is part of the Basel framework (IRB approach) and has been used to evaluate CDOs.

Imagine you loan money to a friend who will default with a probability of 1%. When it comes to paying back the loan you will either receive 100% (plus any interest) or 0%. That's pretty risky. So you figure you can improve your situation by making same size loans to n friends. (NB: You will need a license for doing so). In case they all default individually with a probability of p = 1%, the law of large numbers tells you that the more loans you make (increase n), the closer the average default rate (= portfolio default rate) will be to 1%. "The" central limit theorem states that the portfolio default rate will be normally distributed with a mean of 1% and a variance that goes to zero as n increases.

Now here is the result for n = 5000 loans and 100,000 simulations (portfolios):
vasicek01
Unfortunately, this is only true when default solely happens due to idiosyncratic reason such as illness or a divorce, i.e. when the default of one friend is not related to the default of another friend. But in case you make loans to colleagues from work this assumption won't be correct since bankruptcy of the company would turn most of your loans sour at the same time no matter how large (number of obligors) your loan portfolio actually is. In other words: Certain systemic risk can't be diversified away.

Assuming you really have lots of "similar" friends (p = 1%) and they are all pretty evenly distributed across the sectors the economy has to offer one could argue that defaults are actually only a function of this idiosyncratic risk (as before) and a single systemic risk factor reflecting the overall state of the economy. In case the economy does very well, hardly anybody will default (even an expensive divorce is not an issue) and in case the economy enters into a deep recession, the default rate goes north. The sensitivity of each obligor to this systemic factor and the correlation among the obligors is given by √ρ and ρ, respectively.

Result for n = 5000 loans and 100,000 simulations (portfolios):
vasicek02vasicek03
The average portfolio default rate is not affected by an increase in correlation, but the higher the correlation the more likely extreme portfolio default rates become (good or bad). In case the correlation is one, we are back to a single obligor. Either nobody (0%) or everybody (100%) defaults.

The model (see comment section for details) is a useful starting point but since both systemic and idiosyncratic risk is assumed to be normally distributed and are connected via an uncertain correlation coefficient you could easily be on the wrong end of the trade. NB: That doesn't mean the Basel guys did a bad job. They had two parameters (correlation and systemic shock size) for calibrating the model.
Mahalanobis meinte am 3. Mar, 15:02:
The Model
Assume every friend i earns a certain return Ri each year. When this return drops below a given cut-off level ci, he will default on the loan, i.e. the respective default probability is:



As we've said before, we want the return to be a function of the overall state of the economy and something that reflects idiosyncratic risk which is independent of the state of the economy.



The overall state of the economy is denoted by Y (= systemic factor) and the idiosyncratic shock by εi. The squared "beta", ρ which lies between 0 and 1, tells you the importance of the systemic factor relative to the idiosyncratic one.

Usually, we don't have any good empirical data to calibrate this model. So we make the following assumption:
  • Everybody is exposed to systemic risk to the same extent, i.e. the correlation coefficient ρ is the same for everybody. (A kind of average...)
  • Every individual defaults with the same probability pi = p and this unconditional default probability is known to us (i.e. the portfolio has to be somehow homogeneous, like "only BBB corporates")
  • Y and εi follow a standard normal distribution.
Given that Y and εi follow a standard normal distribution, we know that Ri must follow a standard normal distribution as well*. Given that Ri follows a standard normal distribution and we know the unconditional default probability, p, we can infer the cut-off value c which is just a quantile of the standard normal distribution. In case the unconditional default probability is 2%, the cut-off value is qnorm(0.02) = -2.05



And that's all we need! Now we can ask: Given that we know the unconditional default probability, p, and the correlation, ρ, how does the distribution of the portfolio default rate look like for a large portfolio (see blog post)?

Regulators are usually looking at this problem from a stress testing point of view. They ask: How many defaults would you have, in case Y turns out to be really bad, e.g. a 1 in a 100 years event (y = qnorm(0.01)= -2.33)?

What's so neat about the Vasicek model is that given Y, R is normally distributed with a variance that goes to zero as n goes to infinity! So given that you know Y and given your portfolio is very large, you can actually calculate your portfolio default rate given the unconditional default rate:



related items:
The Merton Model (Moody's KMV) : Video : David Harper, Bionic Turtle

Source:
Kreditrisikomessung, Henking et al., Springer, 2006
Kreditderivate und Kreditrisikomodelle, Martin et al., vieweg, 2006

* E(Ri) = 0, Var(Ri) = 1, and a linear combination of two independent standard normal distributed random follows a standard normal distributin as well. 
davidpool antwortete am 23. Apr, 10:15:
I can't draw, read tarots, nor have I an understanding of genealogy. My real girlfriend would be furious and confused if I hired myself out as a Facebook girlfriend to a stranger. I'm also scared of fire. fiverr featured gig 
BlackMen (guest) antwortete am 21. May, 17:03:
BlackMen
What's so neat about the Vasicek model is that given Y, R is normally distributed with a variance that goes to zero as n goes to infinity! So given that you know Y and given your portfolio is very large, you can actually calculate your portfolio default rate given the unconditional default rate: buytherc.com 
citigo reklama (guest) antwortete am 29. May, 12:13:
What's so neat about the Vasicek model is that given Y, R is normally distributed with a variance that goes to zero as n goes to infinity! So given that you know Y and given your portfolio is very large, you can actually calculate your portfolio default rate given the unconditional default rate: citigo reklama 
High Pr Backlinks service (guest) antwortete am 8. Jun, 10:00:
istributed with a variance that goes to zero as n goes to infinity! So given that you know Y and given your portfolio is very large, you can actually calculate your portfolio default rate given the unconditional default rate: 
www.eczemafreeforever.org.uk (guest) antwortete am 14. Jun, 14:07:
I can't draw, read tarots, nor have I an understanding of genealogy. My real girlfriend would be furious and confused if I hired myself out as a Facebook girlfriend to a stranger. I'm also scared of fire. www.eczemafreeforever.org.uk 
Mahalanobis meinte am 3. Mar, 18:07:
R Code
n <- 5000
t <- 100000
rho <- 0.3
p <- 0.01

port.def <- array(0,t)
for(i in 0:t)
{
y <- rnorm(1)
e <- rnorm(n)
r <- sqrt(rho)*y + sqrt(1-rho)*e
port.def[i] = length(r[r<qnorm(p)])/n
}

# Plot histogram
library(MASS)
truehist(port.def, xlim=c(0,0.1), xlab="portfolio default rate", main="Vasicek Distribution, p = 0.01 and rho = 0.3") 
sodik (guest) antwortete am 7. Apr, 12:20:
I am preparing a research paper and collecting information on this topic. Your post is one of the better that I have read. Thank you for putting this information into one post.
alfamart official partner merchandise fifa piala dunia brazil 2014
Unit Link Terbaik di Indonesia Commonwealth Life Investra Link 
poollaw antwortete am 29. Apr, 14:57:
This is my story of how I had Victoria's Beckham's body for a night. I have given up on all the weight loss methods that have tried and sadly didn't work and believe me, I've seen a lot of them. From diet pills to crash diets to different exercise regimens bodyslimmd 
poollaw antwortete am 29. Apr, 14:58:
These cards are legitimate and they are FREE. When card holders present the discount card to their pharmacist they will receive a discount of up to 85% on their medications. Discounts average 15% on brand name drugs and 55% on generics. Over 80% of the pharmacies in the U.S. participate in this program. bostondiscountcard 
begedir antwortete am 4. May, 19:26:
I am preparing a research paper and collecting information on this topic. Your post is one of the better that I have read. Thank you for putting this information into one post. cara belajar bahasa inggris dengan cepat , pengen cepat hamil , kata kata minta maaf 
davidpool antwortete am 14. May, 12:24:
www.guru4travell.com
Exactly the reason why perhaps not really take a few of the burden from yourself through enabling your loved ones members that will help you in your own daily work. Here are a few ideas that you could put in to action to begin obtaining your own household included. www.guru4travell.com 
davidpool antwortete am 14. May, 12:24:
Many shops charge an excessive amount of for these kinds of products. Try foldable your clothing in innovative methods will occupy less room. Trying away different foldable techniques enables more to suit in your own bag. schoolperform.com 
davidpool antwortete am 14. May, 12:24:
The method of automobile shopping can be extremely stressful proper. There are usually endless variety of vehicles to take into account, and it really is normal to be able to feel confused. The details here may help make investing in a car since easy and also stress-free as you can. businesscarsview.com 
davidpool antwortete am 14. May, 12:24:
Purchasing a car from exclusive parties is a superb choice, but use a mechanic offer it any once above. If the particular owners is not going to enable you to do this kind of, consider that a reddish flag. This generally means there are issues they are attempting to cover upwards. auto-mortgage.com 
davidpool antwortete am 14. May, 12:24:
Finding the most effective solution regarding auto repair may be simple by following tips previously mentioned. Keep carrying out research with this topic and discover people who is able to teach that you simply few items. The more you understand about automobile repair, the far better off you will end up. electus-auto.com 
BlackMen (guest) antwortete am 5. Jun, 15:30:
BlackMen
Beckham's body for a night. I have given up on all the weight loss methods that have tried and sadly didn't work and believe me, I've seen a lot of them.Driving school in costa mesa ca 
BlackMen (guest) antwortete am 7. Jun, 08:46:
BlackMen
The sensitivity of each obligor to this systemic factor and the correlation among the obligors is given by √ρ and ρ, respectively. cambogia garcinia dr oz 
BlackMen (guest) antwortete am 8. Jun, 08:59:
BlackMen
Brazil cannot do much about soybeans during this time if not for selling part of the upcoming crop.cydia sources 2016 
BlackMen (guest) antwortete am 8. Jun, 10:54:
BlackMen
Trying away different foldable techniques enables more to suit in your own bag. aparateaerconditionat3.blogspot.com 
BlackMen (guest) antwortete am 9. Jun, 14:11:
BlackMen
Beckham's body for a night. I have given up on all the weight loss methods that have tried and sadly didn't work and believe me, I've seen a lot of them.Click for information 
BlackMen (guest) antwortete am 10. Jun, 09:08:
BlackMen
They had two parameters (correlation and systemic shock size) for calibrating the model.soccer gadgets 
BlackMen (guest) antwortete am 24. Jun, 15:47:
BlackMen
I am preparing a research paper and collecting information on this topic. Your post is one of the better that I have read. http://horseracing.about.com/od/latestnews/ss/aa-2014-Oaklawn-Handicap_6.htm 
men's clothing (guest) antwortete am 28. Jun, 11:58:
good blog thank you for the post. the world's fashion is the handbags are it is the jewelry and 
Chris Attardo (guest) antwortete am 16. Jul, 09:23:
Health
Zev Wolmark : is a knowledgeable and adviser in the field of finance. He has worked with several massive names and respected personality within the domain for his resolution providing talents, in toughest of matters. For more information visit us @ zevi-wolmark.brandyourself.com. 
BlackMen (guest) antwortete am 24. Jul, 06:24:
BlackMen
Vasicek model is that given Y, R is normally distributed with a variance that goes to zero as n goes to infinity! So given that you know Y and given your portfolio is very large, you can actually calculate your portfolio default rate given the unconditional default rate:Acoustic Sound Insulation Testing 
BlackMen (guest) antwortete am 3. Aug, 13:45:
BlackMen
hardly anybody will default (even an expensive divorce is not an issue) and in case the economy enters into a deep recession, the default rate goes north. The sensitivity of each obligor to this systemic factor and the correlation among the obligors is given by √ρ and ρ, respectively. Dave Morin 
toothless plush (guest) antwortete am 28. Aug, 14:41:
test
I feel like many people out there do not know this much info about it. I am thankful that someone like you can elaborate on this topic. 
free male enhancement samples with free shipping
Just about all penis stretcher devices currently available are just about all built on a single principle. By extending the manhood gently on the set time period, the penises cells is going to be stimulated and can encourage development in both girth and length. free male enhancement samples with free shipping 
volleyball (guest) antwortete am 16. Sep, 10:25:
volleyball
In the most glorious international match in volleyball history, Cuba beats the U.S. 3-2 (17-15, 15-7, 11-15, 9-15, 15-10) for the IX Pan American Games gold medal in the Venezuelan capital of Caracas in August 1983; the nation's first Pan American medal in 16 years. volleyball 
dsquared (guest) meinte am 4. Mar, 19:12:
Quants vs analysts!
Unfortunately, this is only true when default solely happens due to idiosyncratic reason such as illness or a divorce, i.e. when the default of one friend is not related to the default of another friend.

This is why you quants will always need one or two streetwise neanderthals like me about, to remind you that there are all too many cases where the divorce of one set of friends is intimately related to the divorce of another set of friends! 
Mahalanobis antwortete am 5. Mar, 21:04:
Set of friends
I've actually thought about that! I work for a pretty small organization but at least twice a year a woman goes on maternity leave because she got pregnant from a co-worker. And homicide statistics tell us that you are most likely to get killed by somebody you know.

I often have to think of what a philosophy professor and old friend of mine once told me: You can have as many extramarital affairs as you like. This might even be good for your relationship. But keep one thing in mind: Never ever shit in your own backyard!

The only reason why quants would stop listening to streetwise analysts is that at one point they would have to admit that an educated guess beats a sophisticated model more often than not... 
BlackMen (guest) antwortete am 6. May, 13:42:
BlackMen
In case the economy does very well, hardly anybody will default (even an expensive divorce is not an issue) and in case the economy enters into a deep recession, the default rate goes north. The sensitivity of each obligor to this systemic factor and the correlation among the obligors is given by √ρ and ρ, respectively. vacuum reviews 
BlackMen (guest) antwortete am 21. May, 08:01:
BlackMen
The sensitivity of each obligor to this systemic factor and the correlation among the obligors is given by √ρ and ρ, respectively. Caravans West 
BlackMen (guest) antwortete am 30. May, 10:49:
BlackMen
we don't have any good empirical data to calibrate this model. So we make the following assumption: hillford 
BlackMen (guest) antwortete am 1. Jun, 17:48:
BlackMen
The sensitivity of each obligor to this systemic factor and the correlation among the obligors is given by √ρ and ρ, respectively.IvansTips.com 
BlackMen (guest) antwortete am 5. Jun, 15:07:
BlackMen
The sensitivity of each obligor to this systemic factor and the correlation among the obligors is given by √ρ and ρ, respectively.regime da usp 
BlackMen (guest) antwortete am 11. Jun, 08:09:
BlackMen
The sensitivity of each obligor to this systemic factor and the correlation among the obligors is given by √ρ and ρ, respectively. van hire 
thank (guest) meinte am 21. May, 19:19:
The wig is widespread within the present day style. Therefore, there are many times more in a craze, much less a necessity. A report celebrities and pros work represent unique types transmit hair wigs at random for their interest in the mind of hair trend. The option of sporting a wig specific provision depends on the occasion. Personally, it reflects the taste of the person. Other factors as the availability of many wigs sorting depends on the color of skin with adult men and women and their character outside their preferences effect. Right listed here are some important points about this well known for understanding hairpiece 
Turnkey Solution (guest) antwortete am 16. Sep, 13:47:
Year 2012 has been quite eventful. SRSG also witnessed events and evolved in terms of business verticals, technologies, people and processes.
News room automation
Broadcast automation 
BlackMen (guest) antwortete am 29. May, 12:08:
BlackMen
I an understanding of genealogy. My real girlfriend would be furious and confused if I hired myself out as a Facebook girlfriend to a stranger. I'm also scared of fire. cartier replica watch 
BlackMen (guest) antwortete am 12. Jun, 12:23:
BlackMen
The sensitivity of each obligor to this systemic factor and the correlation among the obligors is given by √ρ and ρ, respectively. http://ireport.cnn.com/docs/DOC-1116955 
BlackMen (guest) antwortete am 18. Jun, 09:52:
BlackMen
My real girlfriend would be furious and confused if I hired myself out as a Facebook girlfriend to a stranger. I'm also scared of fire.web design miami 
wholesale buttons (guest) meinte am 25. Oct, 09:44:
wholesale buttons
A last bit of trimming Flag Buttons concerns the lapels. Most jacket natural Coconut Buttons lapels include a button hole on the Shell Buttons left lapel, roughly an inch below the Wood Buttons gorge,which is generally crystal Glass Buttons sewn shut.On very high quality jackets,Metal Buttons pmya999 there will be a corresponding Overcoat Buttons button on the right lapel,though Pearl Buttons this is merely an element of style,Plastic buttons as the lapels of a suit jacket are never clothing buttons turned up in the manner of a military uniform.wholesale buttons On most any suit,the buttonhole cheap buttons can be opened, and on the very best. 
yellow throw pillows (guest) meinte am 22. Dec, 14:15:
great post
A very awesome blog post. We are really grateful for your blog post. You will find a lot of approaches after visiting your post. I was exactly searching for. Thanks for such post and please keep it up yellow throw pillows 
iphone 5c cases (guest) antwortete am 2. Jan, 13:22:
Great post
Thanks for your great sharing and I hope you will more famous day by day. My all the best for your legendary writing.iphone 5c cases 
oliver (guest) antwortete am 20. Feb, 13:49:
Yacht charter Sukosan is not only one of the best sailing destinations in Croatia and the entire Adriatic, but also one with the longest history, since it has played the role of touristic resort since medieval times yachtchartersukosan.com 
BlackMen (guest) antwortete am 24. Jul, 18:12:
BlackMen
A very awesome blog post. We are really grateful for your blog post. You will find a lot of approaches after visiting your post. Read this page 
personalized gifts for men (guest) meinte am 29. Dec, 16:38:
Great post
This is the very good idea! Just want to say thank you for information, Just continue to the write such a position. I will be your faithful reader. Thank you again. personalized gifts for men 
maskodok antwortete am 15. Jan, 00:59:
Each of the front line engines and tenders had the transmitting development changed. This recommendation led to benefits for braking mechanism m aintenance and enhanced avoiding ability.
Mobil Sedan COrolla,Texas Online Indonesia Terpercaya, Mobil Sedan COrolla, Cipto Junaedy 
BlackMen (guest) antwortete am 24. May, 10:07:
BlackMen
'Analog Heaven', Bob Moog discusses not only the development and early days of the Model D but also the monolithic Moog Modular systems that launched the company into the popular consciousness. Buy Traffic 
Cleaning Service Chicago (guest) meinte am 5. Jan, 15:43:
Great post
I also much like the design and style of your blog concept. It is actually very very clear and simple to operate.
Cleaning Service Chicago 
home improvement (guest) antwortete am 8. Apr, 07:55:
The basic needs that most of the people have it comes to bathroom fittings is that it needs to be of excellent design, and it needs to withstand the weight of the person. Bathroom fittings can consist of frameless doors and shower curtains, but nowadays, there are a lot of other styles that have become incorporated. home improvement 
leesa meinte am 26. Mar, 07:08:
Great blog article about this topic,I have been lately in your blog once or twice now.I just wanted to say hi and show my thanks for the information provided…
Softy maker
Softy maker manufacture 
Ahmad (guest) antwortete am 15. Apr, 14:47:
Stand in the proper position in order to make your golf game better. Your stance is the number one determinant of ball flight distance. The ball won’t go far if you are slouched too much or too little. sport-only.com 
Ahmad (guest) antwortete am 15. Apr, 14:47:
Learning to read the formation used by the opposing team is essential when playing is crucial if you play defense. You can anticipate the play by looking at where the receiver is. Watch pro games and keep a playbook of their plays. pariersports.com 
Ahmad (guest) antwortete am 15. Apr, 14:48:
This wise decision is one that many individuals have found to be a smart one for both business and personal reasons. There are some important things you may want to know. computervideoservices.com 
leesa meinte am 26. Mar, 07:10:
Excellent and wonderful organic fertilizer for vegetables read! Your article is the best medicine for cattle one I have learnt, and it has high nitrogen fertilizer helped me. Keep doing garden fertilizer that. 
leesa meinte am 26. Mar, 07:11:
Wow chicken incubator amazing, Nice content poultry incubator I found so many interesting industrial filter manufacturers in india stuff in your blog Lube Oil Filters manufacturers in India especially its discussion Thanks to Lube Oil Filters supplier sharing thanks! 
jimspider (guest) meinte am 28. Apr, 12:15:
if you prep yourself ahead of time with the right knowledge and understanding. The work and cost involved in maintaining a home, from minor repairs 
maire (guest) antwortete am 25. Aug, 11:12:
I¡¦ve been exploring for a little bit for any high-quality articles or blog posts on this sort of house . Exploring in Yahoo I finally stumbled upon this site. Reading this info So i¡¦m satisfied to express that I’ve a very excellent uncanny feeling I discovered exactly what I needed. I such a lot definitely will make sure to do not overlook this site and provides it a glance on a constant basis.
zesttravel.org |
 
http://www.zabusinessfromhome.com (guest) antwortete am 8. Sep, 11:13:
I'm impressed, I must say. Very rarely do I come across a blog that's both informative and entertaining, and let me tell you, you've hit the nail on the head. Your blog is important; the issue is something that not enough people are talking intelligently about.
http://www.zabusinessfromhome.com |
 
Lloyds Fraud number (guest) meinte am 8. May, 10:27:
william
via an uncertain correlation coefficient you could easily be on the wrong end of the trade. NB: That doesn't mean the Basel guys did a bad job. They had two parameters 
BlackMen (guest) antwortete am 4. Jun, 08:49:
BlackMen
That doesn't mean the Basel guys did a bad job. They had two parameters celeb surgeries 
BlackMen (guest) antwortete am 10. Jun, 12:06:
BlackMen
That doesn't mean the Basel guys did a bad job. They had two parameters..http://marketic.co 
jimspider meinte am 12. May, 12:02:
A large part of fashion depend on shoes,heels,boots and others. Young girls are very much serious for there fashion. Not only young girls, but also corporate women and all ages women are conscious for there fashion.
commotionsickness |
cottageonmobilestreet |
motherfriendlytexas |
sinkorswimphiladelphia |
dallas-paragliding |
jukasastudiosofficialsite |
pileandcompanyconsulting |
autismegrandecause2012 |
realizzazionesitiwebitalia |
lavillamaillot |
 
MAydi (guest) antwortete am 19. Aug, 08:55:
It is a general fact that every journalist out there try's to find the most relevant world news. But it certainly is hard to find one. It involves a number of factors. From media sources to the event and from asking questions to taking answers, everything has to be on time and properly planned. www.orkneynewstoday.org 
ttlwu meinte am 14. May, 11:42:
I think
This was really an interesting topic and I kinda agree with what you have mentioned here!
https://www.rebelmouse.com/conversationchemistry/ 
maire (guest) antwortete am 25. Aug, 11:13:
Hi there, You have done an incredible job. I’ll certainly digg it and personally suggest to my friends. I am sure they’ll be benefited from this website.
mytraveldna.org |
 
Must say that overall I am really impressed with this blog. It is easy to see that you are passionate about your writing. If only I had your writing ability I look forward to more updates and will be returning.
http://www.consciousbusinesspromotions.com |
 
ttlwu meinte am 17. May, 12:44:
I think
I high appreciate this post. It’s hard to find the good from the bad sometimes, but I think you’ve nailed it! would you mind updating your blog with more information?
text your ex back michael fiore book review 
shona (guest) antwortete am 20. Aug, 09:47:
As Bogusław said, this mod will probably never come out.
turnermotorsportsllc |
 
http://www.stpetehealth.com (guest) antwortete am 1. Sep, 07:06:
Hi there, its pleasant article about media print, we all understand media is a fantastic source of information.
stpetehealth |
 
http://www.unbearable.biz (guest) antwortete am 18. Sep, 07:49:
You might write about the services on the blog. You should disclose it's refreshing. Your blog conclusion could accelerate your shoppers.
http://www.unbearable.biz |
 
ttlwu meinte am 22. May, 13:16:
rebelmouse
It proved to be Very helpful to me and I am sure to all the commentators here!
bail bond orange 
BlackMen (guest) antwortete am 24. May, 10:09:
BlackMen
Revenue increased to $10.3 billion from $9.7 billion last year, with a high concentration of its revenue from its Medicare Advantage business, the company said. Buy Traffic 
MAydi (guest) antwortete am 19. Aug, 08:56:
For a successful business, it is essential to do right marketing, especially when online. There are some really effective marketing methods, which give extraordinary results if applied. www.micronewsagency.org 
jimspider (guest) meinte am 23. May, 12:54:
High school graduation is near and you’re about ready to move on to college. Not all schools are the same, so your choice can affect your education quality. Read on to learn how to choose the right for you.
probusiness-cis.com |
probusiness-ag.com |
dorchestersc4business.com |
inspiredbusinessconference.com |
businessmerch.com |
thirsk-business.com |
servissimbusiness.com |
adamsbusinessconsulting.com |
businessresultimprovement.com |
businessdevelopmenttoronto.com |
 
Plombier Paris (guest) meinte am 23. May, 20:40:
default (even an expensive divorce is not an issue) and in case the economy enters into a deep recession, the default rate goes north. The sensitivity of each obligor to this systemic factor and the correlation among the obligors is given by √ρ and ρ, respectively. Plombier Paris 
ttlwu meinte am 25. May, 12:53:
I think
Interesting post. I Have Been wondering about this issue, so thanks for posting. Pretty cool post.It 's really very nice and Useful post.Thanks
evan sharboneau's trick photography and special effects program 
www.condo-law.us (guest) meinte am 3. Jun, 13:06:
www.condo-law.us
Really great post. I as of late uncovered your weblog and longed to say that I have truly gotten a charge out of surfing around your online journal passages.
condo law 
maire (guest) antwortete am 25. Aug, 11:05:
Hi there, You have done an incredible job. I’ll certainly digg it and personally suggest to my friends. I am sure they’ll be benefited from this website.
traveltims.org |
 
http://www.rsnewhomes.com (guest) antwortete am 5. Sep, 08:54:
I am very happy to find this site. I wanted to thank you for this immense read!! I absolutely enjoying every petite bit of it and I have you bookmarked to test out new substance you post. -
rsnewhomes.com |
 
www.ezworkathome.us (guest) meinte am 3. Jun, 13:08:
www.ezworkathome.us
Rattling brilliant arrange and style and extraordinary theme, scarcely anything else we require : D.
ez work at home 
www.familylawassociates.biz (guest) meinte am 3. Jun, 13:10:
www.familylawassociates.biz
Abundantly acknowledged enthusiastic about giving such an amenable thought, post is phenomenal, thats why i have examined it completely...
family law associates 
www.frankxulaw.us (guest) meinte am 3. Jun, 13:12:
www.frankxulaw.us
These are genuinely monster contemplations in about blogging. You have touched some incredible centers here. Any way keep up writing.... 
www.frankxulaw.us (guest) meinte am 3. Jun, 13:13:
www.frankxulaw.us
These are genuinely monster contemplations in about blogging. You have touched some incredible centers here. Any way keep up writing....
frank xu law 
www.getalifthome.biz (guest) meinte am 3. Jun, 13:15:
www.getalifthome.biz
Impossibly powerful post, I totally altogether appreciate this site, continue with it.
get a lift home 
ttlwu meinte am 4. Jun, 12:35:
I wanted to thank you for this excellent read!! I definitely loved every little bit of it. I have you bookmarked your site to check out the new stuff you post.
brustvergrößerung kosten 
MAydi (guest) antwortete am 19. Aug, 08:57:
As a business, art investing can mean quite a return if the piece is held for long enough. Many investors new to the art buying industry have been attracted by the advertising of record art sales which have taken place in recent years. www.businessinarts.org 
ttlwu meinte am 5. Jun, 16:06:
I think
I love what youve got to say. But maybe you could a little more in the way of content so people could connect with it better. Youve got an awful lot of text for only having one or two pictures. Maybe you could space it out better?
lift weights faster by jen sinkler book 
www.ohiohomeinspector.biz (guest) meinte am 7. Jun, 11:25:
www.ohiohomeinspector.biz
Thanks for your personal marvelous posting! I definitely enjoyed reading it, you can be a great author.
ohiohomeinspector 
www.kidz-toyz-store.biz (guest) meinte am 7. Jun, 11:26:
www.kidz-toyz-store.biz
Very quickly this web site will be famous among all blogging and site-building viewers, due to it's nice content.
kidz-toyz-store 
www.livingthegreen.us (guest) meinte am 7. Jun, 11:27:
www.livingthegreen.us
I will make a point to bookmark your site and will in the long run return some time or another. I need to sway you to unquestionably proceed your extraordinary posts, have a decent occasion weekend!
livingthegreen 
ttlwu meinte am 9. Jun, 15:12:
I think
I have recently started a blog, the info you provide on this site has helped me greatly. Thanks for all of your time & work.
best thing to get rid of herpes 
MAydi (guest) antwortete am 19. Aug, 08:58:
Working at home, from home, in your pajamas, in the nude, at the beach, working from bed or the easy chair - these are all the images and joys of home working that Kate and I enjoy and many others too. www.thehomestop.org 
ttlwu meinte am 11. Jun, 13:49:
I think
cheers for the actual article i have recently been on the lookout with regard to this kind of advice on the net for sum time right now so many thanks
hypotheekwinkel 
maire (guest) antwortete am 25. Aug, 11:06:
Valuable information. Fortunate me I found your web site accidentally, and I’m stunned why this twist of fate did not happened earlier! I bookmarked it.
travelredsea.org |
 
http://www.myhomeballarat.com (guest) antwortete am 5. Sep, 08:55:
Just wanted to give a quick shout out and say that I genuinely enjoy reading your articles.
myhomeballarat.com |
 
ttlwu meinte am 18. Jun, 13:00:
I think
This is just the information I am finding everywhere. Thanks for your blog, I just subscribe your blog. This is a nice blog..
buy fake instagram followers 
ttlwu meinte am 21. Jun, 12:55:
Great post, and great website. Thanks for the information!
Rebelmouse.com 
ttlwu meinte am 21. Jun, 13:31:
Great post, and great website.
Great info! I recently came across your blog and have been reading along. I thought I would leave my first comment. I don’t know what to say except that I have.
www Rebel Mouse 
Superb opinie (guest) meinte am 27. Jun, 07:41:
bankruptcy of the company would turn most of your loans sour at the same time no matter how large (number of obligors) your loan portfolio actually is. In other words: Certain Superb opinie 
thscp1122 meinte am 29. Jun, 11:51:
Wow i can say that this is another great article as expected of this blog.Bookmarked this site..
recommended product 
tsflw meinte am 1. Jul, 09:41:
ashley
Thanks for sharing the post.. parents are worlds best person in each lives of individual..they need or must succeed to sustain needs of the family.
immo europe 
deep recession, the default rate goes north. The sensitivity of each obligor to this systemic factor and the correlation among the obligors is given by √ρ and ρ, respectively.http://www.mobilehomesforsale.com 
top sellers (guest) meinte am 18. Jul, 13:02:
normally distributed with a mean of 1% and a variance that goes to zero as n increases.top sellers 
on certain social sites (guest) meinte am 23. Jul, 13:10:
jack13
They had two parameters (correlation and systemic shock size) for calibrating the model. 
storage (guest) meinte am 27. Jul, 08:51:
the default rate goes north. The sensitivity of each obligor to this systemic factor and the correlation among the obligors is given by √ρ and ρ, respectively. storage 
tsflw meinte am 28. Jul, 11:44:
I am definitely enjoying your website. You definitely have some great insight and great stories. back 
Real Estate Palm Harbor Florida (guest) meinte am 7. Aug, 11:49:
Real Estate Palm Harbor Florida
there can be no large amount of "imported inflation." A country with an independent currency should see exchange-rate changes, not inflation, when some Real Estate Palm Harbor Florida 
tsflw meinte am 7. Aug, 13:53:
Thank you so much for the post you do. I like your post and all you share with us is up to date and quite informative, i would like to bookmark the page so i can come here again to read you, as you have done a wonderful job. e cigarette amazon 
tsflw meinte am 9. Aug, 13:18:
it was a wonderful chance to visit this kind of site and I am happy to know. thank you so much for giving us a chance to have this opportunity.. taxi obergurgl 
jimspider (guest) meinte am 11. Aug, 13:53:
probusiness
nice blog 
tsflw meinte am 20. Aug, 15:08:
This blog is really great. The information here will surely be of some help to me. Thanks!.
idiscountseo.com.au 
click here (guest) meinte am 23. Aug, 04:06:
awesome website
Thank you for this blog. That's all i can say..useful information shared... i am very happy to read this article.. thanks for giving us nice info. fantastic walk-through. i appreciate this post
Joey Atlas Symulast
Joey Atlas Cellulite
Joey Atlas
joey atlas exercises
joey atlas symulast exercises
joey atlas cellulite review
joey atlas cellulite program
joey atlas cellulite scam
joey atlas cellulite exercises
cellulite joey atlas
joey atlas DVD
joey atlas cellulite video
How to get rid of cellulite
How to get rid of cellulite on thighs
get rid of cellulite on thighs
get rid of cellulite
cellulite on thighs
How to get rid of cellulite on butt
How to reduce cellulite 
tsflw meinte am 25. Aug, 11:29:
Its a great pleasure reading your post.Its full of information I am looking for and I love to post a comment that "The content of your post is awesome" Great work.
buy targeted twitter followers uk 
tsflw meinte am 27. Aug, 07:43:
This is a great inspiring article.I am pretty much pleased with your good work.You put really very helpful information. Keep it up. Keep blogging. Looking to reading your next post.
cheap bitcoin hosting 
ttlwu meinte am 9. Sep, 16:46:
Thanks for another wonderful post. Where else could anybody get that type of info in such an ideal way of writing?
taxi ischgl