Serving the Quantitative Finance Community

 
User avatar
tombille
Topic Author
Posts: 0
Joined: October 14th, 2007, 4:57 am

Tranche Spread trend. Problem with Model, or problem with Copula?

October 15th, 2007, 9:04 am

Hello everyone, I've recently run into an extremely frustrating problem. I was hoping you fine gentlemen/women might be able to help me out.I am trying to graph the changing tranche spread relationship of CDOs which depends on Correlation in the various tranches (Equity to Senior tranches) for a paper I am publishing. By all logic and common understanding, going from a 0 correlation to a perfect (1) correlation, the equity tranche (0-3%) should have a negative spread slope, whereas the senior tranche (12-20%) should have a positive slope. Mezzanine should show a somewhat positive/flat trend. I'm sure no one disagrees with me on this point.However, the issue I'm having is when I try to replicate this scenario in my CDO One Factor Gausian Copula model and in other Copula models I have, the slopes are downward sloping for the Equity, Mezzanine and Senior tranches. I have to increase the spreads significantly (0-20% for equity, 20%-40% mezzanine, and 40-60% senior...) to get the desired graph. This is of course cheating, and I would like to develop this graph using real data. I am using standard inputs, i.e. recovery rate 40%, interest rate 5%, hazard rate 10%, maturity 5 years, names 125. The reason why I want to replicate this graph is that I want to show the risk assessments of the various tranches depending on Correlation.You can download a copy of my model at www.thecopuloslawfirm.com/CDOvaluation.xls to try see what the issue is. I don't think it's a problem with the model, as I have tried other models, but if you think it might be, please let me know. Also, please see http://www.rotman.utoronto.ca/~hull/Dow ... lModel.pdf, where Mr. John Hull archived what I am trying to do (to prove that I'm not insane ).Hope you are able to help a frustrated man in need. Feel free to message for further details (I tried to make the explanation above as short and simple as possible).ThanksThomas Rasmussen
 
User avatar
slym
Posts: 0
Joined: May 12th, 2003, 8:48 am

Tranche Spread trend. Problem with Model, or problem with Copula?

October 15th, 2007, 9:50 am

Hey, all you guyz out there trying to achieve their thesis & papers to be published !didn't anyone tell you that the CDOs / Correlation market is dead for months ???maybe you could try some volatility surface modeling, sounds better for your resume now ...
 
User avatar
mikeoz
Posts: 1
Joined: September 28th, 2005, 2:58 pm

Tranche Spread trend. Problem with Model, or problem with Copula?

October 15th, 2007, 12:21 pm

The relationship you describe should be the case. It is definitely not an issue with the copula model, so there must be some flaw in implementation.
 
User avatar
tombille
Topic Author
Posts: 0
Joined: October 14th, 2007, 4:57 am

Tranche Spread trend. Problem with Model, or problem with Copula?

October 15th, 2007, 9:39 pm

Thanks for getting back to me. Yes that's what I thought too. But the problem is I've tried everything. Changing every parameter, playing with the hazard rate etc. I've tried about 4 different copula models to no avail (to rule out that the model is not flawed) The values I have been using are pretty standard values too (recovery rate 40%, interest rate 5%, hazard rate 10%, maturity 5 years, names 125). If somebody out there doesn't mind, could you please either download my model (link below), and try to replicate my problem, or try to solve it using your own model. The easy way to test whether it works or not is to just run two simulations, one at 0 correlation and one and .99. The Equity tranche should have a downward slope between the two points, and the senior tranche should have a positive slope...Thanks!Thomas R
 
User avatar
tombille
Topic Author
Posts: 0
Joined: October 14th, 2007, 4:57 am

Tranche Spread trend. Problem with Model, or problem with Copula?

October 17th, 2007, 9:01 am

I figured it out. Rather simple really. I guess I overestimated people on this forum (heard good things). Don't worry, you'll get there eventually :-)Thanks for trying though!Thomas
 
User avatar
HPBarone
Posts: 1
Joined: July 14th, 2002, 3:00 am

Tranche Spread trend. Problem with Model, or problem with Copula?

November 7th, 2007, 5:32 pm

Dear Tombville,Your linkwww.thecopuloslawfirm.com/CDOvaluation.xlsdoes not work.I'd like to compare your results with mine could you please give more details about the exact details of your structure.Is there a point of using 125 names for only one global hazard rate ?Thanks,Henri-Pierre