Serving the Quantitative Finance Community

sarty06711
Posts: 7
Joined: May 14th, 2004, 5:34 pm

### What are copulas and how are they used in quantitative finance?

Please send me a copy also at nyc_big_ben@yahoo.com

list
Posts: 2041
Joined: October 26th, 2005, 2:08 pm

### What are copulas and how are they used in quantitative finance?

It somewhat difficult to connect copula used as mathematical notion with financial counterpart. In mathematical setting one needs joint multivariate distribution. In this case in this case copula is a connection between the multivariate distribution function and its marginal distribution. Here there is only one input: multivariate distribution and marginal distributions could be found from it uniquely by integration. In finance it looks like people are trying to avoid to state that the case they are studied ether very simple,i.e. marginal distributions uniquely definea multivariate distribution function or if a multivariate distribution function is could not be explicitly found there exist a fat chance that the set of marginal distributions are put into copula from another multivariate distribution function. In the later case this will not a distribution function.

yandong2020
Posts: 12
Joined: November 28th, 2008, 12:02 pm

### What are copulas and how are they used in quantitative finance?

Hello Mr. Melchi,Would you bother to send me your spreadsheet? Many thanks!yandong2020@gmail.com

narkar
Posts: 1
Joined: February 26th, 2009, 8:00 am

### What are copulas and how are they used in quantitative finance?

Dear all,I definitely need your advice. i work at the university as a research assistant(department of int. economics), and the initial topic of my dissertation was supposed to be about the current financial crisis. However, i got digging into financial contagion recently and got absorbed in the world of copulas. I am quite surprised by the extent of the applications of copulas and would like to base my research on them. However, I don't have a degree in math or smth (economics and finance instead), so I would like to ask those who intensively deal with copulas and their applications to advise me whether I would cope with it or it is only (financial) mathematicians who can handle it.Thanks in advance!

HNK
Posts: 11
Joined: February 1st, 2008, 12:30 pm

### What are copulas and how are they used in quantitative finance?

leocabbage
Posts: 5
Joined: September 23rd, 2008, 7:26 am

### What are copulas and how are they used in quantitative finance?

QuoteOriginally posted by: tristanreidA 2 dimensional copula that maps from [0,1]^2->[0,1] has the 3 following properties (from Nelson's introduction):1. For every u in [0,1] C(0,u)=C(u,0)=02. For every u in [0,1] C(u,1)=u and C(1,u)=u3. For every (u1,u2),(v1,v2) in [0,1]x[0,1] with u1<=v1 and u2<=v2 C(v1,v2)-C(v1,u2)-C(u1,v2)+C(u1,u2)>=0Having the first property also means being 'grounded'.Having the 3rd property is also called '2-increasing'.I'm trying to upload a picture of a copula, but I don't see an 'attach' button anywhere.You can see the properties described above pretty clearly from a picture.If you have octave or matlab, here's a function to produce a pretty copula graph (for matlab, take out all the 'g's!):##this is how many steps to put in the function, set it to whatever you want.n=40; ##this is theta. this is a Gumbel-Hougaard copula, if you want details I'll post more## in short, you can adjust theta to see a steeper copulat=2; x = y = linspace (0.01, 1, n)'; [xx, yy] = meshgrid (x, y); z = exp(-(((-log(xx)).^t+(-log(yy)).^t).^(1/t))); gset pm3d gset key below gset border 4095 gset surface gset samples 25 gset isosamples 20 gset ticslevel 0 mesh (x, y, z); gset nohidden3d replot view(15,30)-t.I removed all the 'g's, but Matlab still indicates "??? Error using ==> setVector of handles not permitted for set(h)".

mrmelchi
Posts: 26
Joined: July 14th, 2002, 3:00 am

### What are copulas and how are they used in quantitative finance?

I reply post from narkar. I hope is not too late.Which Archimedean Copula is the right one?This paper presents the concept of copula from a practical standpoint. Given the widened use of the multinormal distribution, we argue its inadequacy, while advocate for using the copula as an alternative and better approach. We examine what the copulas are used for within of risk management. Then we expose a guide to choose both the margins and the Archimedean copula that better fit to data. In addition, we provide an algorithm to simulate random bivariate from Archimedean copula. In order to cover the gap between the theory and its practical implementation VBA codes are provided. They are used in a numerical example that illustrates the use of the copula in the pricing of a first-at-default contract. Two spreadsheets accompany to paper, by presenting step by step all practical applications covered.Tools for sampling Multivariate Archimedean CopulasA hurdle for practical implementation of any multivariate Archimedean copula was the absence of an efficient method for generating them. The most frequently used approach named conditional distribution one, involves differentiation step for each dimension of the problem. For this reason, it is not feasible in higher dimension. Marshall and Olkin proposed an alternative method, which is computationally more straightforward than the conditional distribution approach. We present the tools necessary for understand it and use it. We introduce the Laplace Transform and its role in the generation of multivariate Archimedean copulas. In order to cover the gap between the theory and its practical implementation VBA code and R one are provided.I hope this helps.
Last edited by mrmelchi on April 26th, 2009, 10:00 pm, edited 1 time in total.

janneyxu
Posts: 1
Joined: October 23rd, 2003, 11:43 am

### What are copulas and how are they used in quantitative finance?

I'd appreciated if you could send me a copy of that 'famous' speadsheet. The e-mail address: janneyxu@hotmail.com. Many thanks!

joo21
Posts: 1
Joined: February 8th, 2007, 10:12 pm

### What are copulas and how are they used in quantitative finance?

jfuqua
Posts: 1255
Joined: July 26th, 2002, 11:41 am

### What are copulas and how are they used in quantitative finance?

I've never been clear exactly what the problem with copulas in the credit mess was. The obvious things are that they like VaR are trying to give one number that management can use and that the Gaussian distribution is assumed. It also appears that the volume of data for defaults, recovery, and credit instrument was much to small and even if historical data had been used it was also so small that it would not be statistically significant. Also assumptions about independence was wrong. Were the other main problems that not only management but the quants, accounting and even risk people believed and relied on what the copula told them ? They knew it could not be 'right' but figured it was close enough that they did not need to worry ? Thought the housing and corporate boom would never end and other credit protection [counterparty, AIG and other insurers] was strong enough that counterparty risk was not significant and relying on the accuracy of the credit rating agencies, esp. with the SPV ratings they could get from the agencies. I.e. "drinking their own cool-aid." Copulas are a well known statistical method but like any use of stats or math, can be mis-used and bad assumptions [Gaussian] and bad/weak data can be used. David Li proposed a method to use copulas for finance but [perhaps much after the fact] warned about what they could and could not be used for. Thus was it really the users rather than the method/assumptions that were the problem ?

jreyesro
Posts: 2
Joined: April 26th, 2010, 4:17 pm

### What are copulas and how are they used in quantitative finance?

Hi Mr Melchiori,I've seen your message in contingencyanalysis.com which says that you have spreadsheets for bootstrapping and interpolating yield curve using linear and spline, and I would like get your spreadsheets about Copulas, too. Could you send me those spreadsheets to julio.reyes@subuschile.cl?Thanks a lot

Henderson
Posts: 23
Joined: October 26th, 2006, 2:56 pm

### What are copulas and how are they used in quantitative finance?

Can I get a copy of the spreadsheet as well? Many thanks! Henderson.geoffrey@gmail.com

sachintodkarus
Posts: 1
Joined: February 26th, 2010, 2:37 pm

### What are copulas and how are they used in quantitative finance?

I would also like to have the spreadsheets for bootstrapping and interpolating the yield curve. Can you please send it at sachintodkarus@yahoo.comThanks in advance.

ae8812
Posts: 1
Joined: June 25th, 2009, 3:28 pm