# Student t copula in Excel

#### CKCHAN

##### New Member
Hi,..

I am trying to implement Student t copula in excel to price some basket default swap...

However, i just cant seems to get it to work in excel at low degree of freedom, v....just wondering what i do wrong...

Here is the step i took
1) Derive Cholesky decomposition A from the correlation matrix
2) Generate n number of independent standard random variables Z
3) Set x = A*Z
4) Generate a random variate s from chi squared distribution with degree of freedom v.
5) Set y = x*sqrt(v/s)
6) If y <0 , apply Tdist(-y,v,1), otherwise 1 -Tdist(y,v,1)
7) Obtain default times...and price accordingly over m number of simulation

If i set v to be anything between 0<v<60..the answer deviates from a Gaussian Copula by a lot...say a FTD is 100bps for Student t compared to 300 bps for Gaussian...

Can anyone help?

#### bob

##### Faculty (Undercover)
Having never done a t copula before, I decided to give it a whirl. The attached is a very simple implementation for 3 names: It assumes zero interest rates and continuous payments on the premium leg, so obviously it's a tad unrealistic.

But it does price all the single names back to their hazard rates correctly (which I imagine your implementation doesn't if the first-to-default spreads are that far off), and the results pass the smell test, at least at a glance.

No warranty express or implied, of course: I just threw this together when I saw your question. But perhaps it will help.

#### Attachments

• 70.5 KB Views: 311

#### Beata

##### New Member
Hi Bob,
can you please send me your file, because I have the same problem with implementation of t-Student copula and I can not download the file.