Gaussian copula
Вставка
- Опубліковано 30 сер 2009
- The Gaussian copula was gainfully employed prior to the credit crisis, and it has pretty much been shamed. Mathematically, it's an elegant way to join marginal distributions and handle default correlation. But it requires too many simplifying assumptions.
You are the first one to explain it in an understandable way.
Yes!
Yeah, you could have just said a small group of people on this planet have the ability to print money out of thin air and eventually will own everything on this planet, but I guess you can say it the way you said it too… I look forward to the future where all of us will own nothing and we will be happy.
Good to have you back David, you're my favorite subscription on youtube - slowly working my way through all the videos.
I'm here for the new crisis, Corona. The effects off defaults are getting larger and larger... So this still, after 11 years, remains so relevant
Great explanation. just wondering where is the "Joint CDF" number come from (how does the math work)?
The math is simple have the ability to print money out of thin air and you can substantiate any bullshit algorithm even though it is mathematically implausible.... Remember peasant soon you'll own nothing and you'll be happy. There are people a lot smarter than you that know what's best for your life...
Elegantly explained. Keep up the good work.
Another outstanding explanation - thanks so much ! I have the misfortune to have to spend time talking to quants in the City of London, and they seem either incapable or unwilling to make clear the basis of many of the things they do. If only I could take along an app into which they could speak, and you could provide the translation!
For modeling asset processes, Is an iid alpha stable model (alpha
David, for 2 bonds I thought that joint event pd was given using the Bernouilli variable (Jorion, page 460). For instance in your example if correlation is 0.3, then joint pd is 1.67%, with no assumption about bonds pd shape.
do you have a vdo about copula value at risk?
So well explained!
many thanks for your help.
Good Day! Do you also have a video about frank copula? thanks!
Great video. Thanks.
Copulas allow for greater flexibility in modeling marginals and dependency but at a computational cost. So if you have Gaussian Marginals w/ Gaussian copula type dependency, just model it with a multivariate normal distribution.
@bionicturtledotcom could you please be more spesific? unfortunately, i never did these kind of graphs before...
Also another question, does gaussian copula solve the nonlinear correlation problem? i mean i wonder whether the gaussian copula provides linear correlation.
Technical details aside, the video is making a very good point - that Gaussian copulas have an underlying assumption that is generally wrong. The main issue is the behavior in the joint tails, in that it assigns too little probability to bad things happening together. There are plenty of other copulas available, but all the Monte Carlo simulation tools I know, with the exception of the ModelRisk software, use the Gaussian copula to generate correlation.
thanks, very good explanation - i understood all of that.
Hello. Can i ask you something? Do any copula can joint any marginal distribution into a join distribution? Let me make an example. I have two vector random X=(X1, X2) and i want to use t-copula (bivariate t distribution). Do this vector random X should distributed t univariate? Or vector X can be distributed in any distribution and t copula will make them to have bivariate t-distribution? I hope you'll answer my question. Thank you.
Multiple different joint distributions can correspond to the same marginal distribution, however every joint distribution has a unique copula which correctly converts the marginal distributions into the joint distribution. This is Sklar's Theorem.
Where is the link to the xls?
@RefUser as it's an approximation, i can't describe the calcs in < 500 characters (nor do i have the time). But i add a link to the XLS. I think i can share files now by linking to the dropbox file, so look for the excel soon, thanks, David
Bionic Turtle where is the link to the xls?
may i ask some more question? it's what makes gaussian copula superior to correlation from normal distribution. I mean from theorem we know that if each data set is normal, joint prob will be normal too. then why should we use copula parameter instead of using rho of normal distribution itself.
Under a Gaussian type dependency structure, as the irregularity of the event increases said event's dependency goes to zero (asymptotic tail independence==>uncorrelated extreme co-movements). This leads to illusory gains from diversification/network densification. Given the non-monotonicity of systemic fragility if diversification is coupled with an endogenous financial accelerator, excess diversification increases risk irrespective of super-heavy tailedness w/ insufficent gain/loss asymmetry.
Which is the advantage of gaussian copula vs normal distribution?
Hi Bionic Turtle, your explanation have helped me to understand the Gaussian Copula greatly. May I know where to find the excel file for your Gaussian Copula graph, or how to make one?
Thanks.
Given he is using a Gaussian copula coupled with Gaussian marginals which is equivalent to a bi-variate normal distribution,===> if p=0, then X,Y are independent random variables.
great explanation
how did you make the graph?
thanks alot. I've always wondered what gaussian copula is.
@ditke71
AFAIK
Copulas do not make any assumptions about the form of marginal distributions. It only makes assumptions about the form of the relationships between the marginals. The Gaussian copula does not assume that the marginals have normal distributions.....otherwise there would be no difference between multivariate normal distribution and Gaussian copula.
Hope that was helpful and if anyone thinks I am wrong I am open to discussion.
@Bhavan71
Yes, I know, but Gaussian Copula uses the correlation cofficient in its expression. The marginals could be any univariate continuous marginals. But the question is, if it has any sense to use the correlation coefficient if the joint probability distribution is not normal.
So in my opinion, this is why the Gaussian copulas did not work.
hi, can you please share the excel file? it would greatly help with my understanding of the formula
Great explanation
@RefUser It's just excel (assuming you don't mean the officedraw or conceptdraw at the beginning). And I do (totally) agree with oringent's technical criticism: it's really a graph of bivariate normal pdf. Thanks David
How can i transforme from archimedisnne to normale?
Excellent! Very clear explanation. The normality assumption is the major reason why Gaussian copula failed, but there are Student, Frank and Clayton-Gumbel copulas that do not assume normality, right?
This is awesome! By the way, is the spreadsheet published online? Would love to play with it and develop some intuition
Independence is a stronger condition than uncorrelated.( In most (if not all but one case) independence=>uncorrelated but uncorrelated =/=> independence). If g(x,y) is jointly Gaussian & uncorrelated, then X,Y are independent. It's a very special condition.
Thanks
The entire problem is that it's Gaussian and the distribution. It's elegant in it's multi-variate capabilities. Yet, anything financial calls for non-gaussian and non-linear.
It's why we're running into these events much more often than what the models call for
The risk models are exactly as you point out ... a standard normal distribution
very easy to understand with great visualization. You just save my ass :))
2:30 how come we are unable to multiply 5% by 5% when the correlation changes to .3?
Because they are no longer independent events if they are correlated. You can only multiply probabilities like that under the assumption of independence. For instance, if the correlation = 1, they are perfectly correlated (essentially mirror each other). So whenever one bond defaults, so will the other, the probability then would just be 5%.
Are you trying to make mathematical sense of a fraudulent financial structure where some individuals have the ability to print money out of thin air and others don't?…. I remember we would use these pseudo mathematics in Deutsche bank's lawsuits against people who were figuring out what we were doing LMFAO... Soon you'll owe nothing and you'll be happy.
@@1337vIKz can you help me with the formula of joint probability but with correlated events?
The Gaussian Copula affords us the ability to deal with non-Gaussian marginal distributions. It is the same kind insufficient generalization as fractional Brownian motion which induces long memory at the cost of excess smoothness/nil quadratic variation. It is extremely inferior because unlike many other copulas it is exogenous, symmetrical and has zero tail dependency irrespective of the degree of correlation.
If I had the ability to print money out of thin air I would hire someone like you to use pseudo intellectualism to cover for my criminality... But then again who cares soon me and you both will own nothing and will be happy.
@@JohnAdams-mu7xd Completely unrelated
@@axe863 You know why it's completely related is because your mathematical theories which are nothing more than theories are literally used to substantiate fraudulent financial markets by using nonsense statistical math like the gaussian copula... You start with baseless data points which you know have some dependence (but not what sort of dependence) you do not know the distribution of each data set by itself either. You look at it and try to figure out the distribution that best APPROXIMATE its behavior, once you have settled on one particular distribution you use its relevant cdf function to magically transform both of them to a uniformity distributed observations, then you try to figure out the correlation between both uniform bullshit datasets, but to give a final twist, you use a function instead of a constant value for fictional correlation, and that function is the supposed copula...🤦♂️
Sorry if I kind of came off like I was attacking you but I used to litigate on behalf of Deutsche Bank to prevent counter lawsuits of people alleging securities and commodities fraud and we would always bring in so-called expert witnesses to complicate things with pseudo mathematics so that the courts would drop the allegations... Just so you know nonsense math like this helped exacerbate the issue of synthetic collateralized debt obligations and the massive financial wealth transfer of 2008... My bad if I came off as a dick.
@@axe863 "The study of money, above all other fields in economics, is one in which complexity is used to disguise truth or to evade truth, not to reveal it” John Kenneth Galbraith
@bionicturtledotcom thanks!
At the beginning, when you show the "0 correlation", you say "the variables are independant". This is not true. Two variables that have 0 correlation are not necessarly independant. But if they are independant they have 0 correlation.
linear independent
(eating popcorn) 0~0 *munch*... *munch*
Oh ok, I misunderstood what you meant.
What you are graphing there is actually not the copula but the bivariate normal pdf. The marginals of the copula are continuous uniform[0,1] distributions. The whole idea of copulas is to isolate the dependence structure from the marginals. It is completely irrelevant weather or not financial returns are normal. Using Gaussian Copulas to model financial assets does not make this assumption, it only makes the assumption that the dependence structure is well approximated by the Gaussian copula.
For a correct explanation of Gaussian Copula see Wikipedia. Incidentally, a copula is not a density (as graphed here) but a cumulative distribution function with support in some "n dimensional [0,1] space"
This is true in this case, yes. Not as a general statement, that's what I meant.
"In the case of the gaussian copula, we're making the huge assumption that [the marginals distributions are] described by a normal distribution"
This is completely WRONG!!! The very purpose of the copula is being able to study the dependence of 2 variables independently from the marginal distributions. E.g. the marginals could have been student-t distributed...
Anas Guerrouaz Thank you, captain obvious. For large portfolios, the optimal method for static parameter models is a Mixture Pair Copula Construction structure because there is varying dependence structure between asset pairs and parametric Elliptical and Archimedean copula classes are too restrictive.
axe863
In addition to using words you cannot understand, you're not addressing the issue I have pointed out in my comment. But thank you for sharing your Elliptical knowledge, jerk.
Anas Guerrouaz
I already commented on that error years ago. You could have waded through the few comments and found where I made the same statement.
axe863
Of course. I mean what kind of person doesn't read comments from years back when they watch an online video?
Get a life.
Anas Guerrouaz Hello. Can i ask you something? Do any copula can joint any marginal distribution into a join distribution? Let me make an example. I have two vector random X=(X1, X2) and i want to use t-copula (bivariate t distribution). Do this vector random X should distributed t univariate? Or vector X can be distributed in any distribution and t copula will make them to have bivariate t-distribution? I hope you'll answer my question. Thank you.
could you please sent me the VBA code behind the result of 0.71% for correlation=0.3? I really would like to study that
David, always enjoy your videos. Very well explained. Just a note: Financial is spelled "finanical" at 7:11. You probably already know this, but in case you didn't, I just thought I'd mention.
"very stubby shaft"
@deskset24 that doesn't even make sense on the common sense level. So what you're saying is that the direct stakeholders in the financial system decided to sabotage their own cash cow? Why? How can you justify your view?
LOL!
Lol, not only don't you understand the very basic concepts of probability you also don't understand sarcasm. It's hilarious how some high school kid like you tries to lecture me based on his flawed understanding. You don't even understand the difference between a random variable and it's density function. You are hilarious, bro.
Lol, yeah that's why he is graphing a bivariate normal and puts a header "Gaussian Copula". Get your shit straight before you start arguing with me kid.