Serving the Quantitative Finance Community

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

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

Suppose:1)The asset prices are log-normally distributed and the percentage asset returns are normally distributed N(0,1).2)We get a realization of two variables uniformly distributed u=0.804172 and v=0.271105 draw from a copula ( Gaussian, t, Archimedean etc).3)Price of the asset A in t0 is equal to tA,0=100 and price of the asset B in to is equal to tB,0=100Then:Convert u and v to pseudo random numbers with distribution function Normal Standard and joint distribution function draws from the prior copula ( Gaussian, t, Archimedean etc). In Excel language:r1=NormSInv(u)= 0.856617r2=NormSInv(v)= -0.609474so that:ln(tA,1)-ln(tA,0)=ln(tA,1) - ln(100)= 0.856617ln(tA,2)-ln(tA,0)=ln(tA,2) - ln(100)= -0.609474tA,1= tA,0 * exp(0.856617/100)= 100.860298 tB,1=tB,0 * exp( -0.609474/100) = 99.392378 so the price of the asset A in t1 is equal to tA,1= 100.860298 and the price of the asset B in t1 is equal to tB,1= 99.392378 .I hope this helps
Last edited by mrmelchi on April 19th, 2004, 10:00 pm, edited 1 time in total.

happySoul
Posts: 2
Joined: February 17th, 2005, 8:20 am

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

Hi mr melchi,Is it possible for you to also send me your spreadsheets.edj3@hotmail.co.ukThanksedj

tristanreid
Posts: 441
Joined: May 12th, 2004, 6:58 pm

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

A 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.

chiron
Posts: 53
Joined: January 11th, 2004, 4:29 pm

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

tom2
Posts: 7
Joined: July 19th, 2005, 8:00 pm

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

Hi everyone,could you please send a copy of spreadsheet to my email address: tzhang_1@hotmail.com.Thanks so much,TZ

creditderivative
Posts: 52
Joined: November 29th, 2004, 9:34 pm

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

Hi there,May I have the spreadsheets too? Thx. Mail

taposhri
Posts: 4
Joined: October 27th, 2005, 12:34 pm

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

Hi Mario,Could you please send me your spreadsheet? My email address is : taposhri@hotmail.comMany Thanks.

vinayboy
Posts: 49
Joined: September 8th, 2004, 2:08 pm

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

Hi Mario,Is it possible for you to mail the sheet to vinayboy@yahoo.com?Many thanks!

swtzang
Posts: 11
Joined: December 2nd, 2005, 3:40 am

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

Hello, may I have a copy of spreadsheet? Thanks.My mail: swtzang@mail.nsysu.edu.tw

vkohli
Posts: 1
Joined: January 19th, 2006, 11:10 am

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

Mario,Can you send me the spreadsheets too ? My email id is vkohli@gmail.com.Varun

Colossus2420
Posts: 28
Joined: February 2nd, 2006, 5:42 pm

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

Mr. Melchi,May I have a copy of your worksheet as well, please? Thanks,JMarsick@OAMAvatar.com

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

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

I know this is late in the game but the original question [or heading] what what are copulas for in finance.Here is a link to a free paper [actually presentation]:http://www.risklatte.com/copula/copula0 ... fCherubini Umberto, Elisa Luciano 'Multivariate Option Pricing with Copulas' for an application outside risk managementHennessy David, Harvey Lapan 'The Use of Archimedean Copulas to Model Portfolio Allocations' MF 4/02

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

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

Try Tools for sampling Multivariate Archimedean Copulas( www.defaultrisk.com/pp_corr_83.htm )I hope it helps.
Last edited by mrmelchi on April 4th, 2006, 10:00 pm, edited 1 time in total.

Posts: 11048
Joined: February 1st, 2005, 11:21 pm

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

What a great website. Many thanks.defaultrisk.com

sihingrich
Posts: 1
Joined: June 8th, 2006, 7:55 pm

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

Hi Mr. Melchi,Can you send me your spreadsheets?Thank you.Richr.borowy@pitcairn.com