CDO Pricing Model of Andersen, Sidenius, Basu

Firebird · August 24th, 2005, 12:59 am

I would also like to reproduce the results from H-W paper. The Appendix B seems not very clear to me. Who can forward CDO pricing paper published on Risk to me? I would really appreciate. I can't find that paper on the internet. Appendix A is a good approach.

mf42 · August 24th, 2005, 10:00 am

Hi, I implemented the semi-analytical approach in C++ and compared the results with MC which are pretty close. Still my problem is the recursion formula. For the unconditional loss distribution I have to evaluate the support points in the gaussian quadrature which leads to a call of the recursion formula for each. Having a portfolio with N companies thisleads to 2^N different events. I already tried to use binary trees, which seems to be an optimal data structure. Still for N > 20 this is not tractable. Any ideas to optimize it? Shall I switch to FFT? Thanks a lot.

wahoo2000 · August 24th, 2005, 12:58 pm

Are you performing the integration before or after the recursion step? I more or less followed ASB, but I definitely had to reorder the steps in the computation. I compute the integral in the very last step and it speeds things up dramatically (in MATLAB at least).

mf42 · August 24th, 2005, 1:47 pm

Well, to compute the unconditional integral one has to evaluate the conditional probabilities for special values (special realizations of \Omega) given by the gaussian quadr. algorithm. This leads to a call for the recursion formula for each realization. Nevertheless, even one call leads to unacceptable calculation time. Maybe a recipe is to cluster the underlyings?

wahoo2000 · August 24th, 2005, 3:47 pm

Quoteeven one call leads to unacceptable calculation time. Define unacceptable? Maybe I am enjoying the benefits of MATLAB's speed on matrix computations, but my code can price a heterogenous 125 name portfolio in less than 3 seconds... what do you mean by "cluster the underlyings"? I perform the recursion simultaneously for all point on my time grid (through Matlab vectorization), so maybe you can try the analogous in C++.

Firebird · August 25th, 2005, 12:12 am

Hi, wahoo2000,Would you forward Anderson, Sidenius and Basu to me? Is semi-analytic methodology in Fabio Mibielli Peixoto's paper very similar to that in Anderson's paper? Thanks.

fodao · August 25th, 2005, 4:17 pm

No. The one is Peixoto's paper is based on the Hull-White proposal. It uses a recursive approach to calculate the default distribution while Andersen et al calculates the loss distribution.

Karwitz · August 26th, 2005, 1:05 pm

Regarding the distribution for X_i when the idiosyncratic and the market factors are t-distributed. I haven't seen anyone suggesting a good approach of finding the distribution for X_i. Since it must be performed in run time the performance is a vital factor and all available techniques I've tried are disqualified because of computing time. Hull and White have advertised this model pretty well and I guess it's something they make a lot of money out of, thus it's not in their interest to reveal the small tiny key missing (a small tiny key of vital importance). I would guess that they use some form of pretty-good-guess-is-good-enough for the distribution of X_i. For example they could assume a t4 distributed X_i or similar for a t4-t4 model.I'm glad others are thinking about this. If you find anything please let us know.

Daspade · August 26th, 2005, 1:35 pm

What about separately generating a cdf with MC (i.e. creating a RV that is the sum of the t distributed variables) then using that to find the inverse?

Karwitz · August 26th, 2005, 2:01 pm

That is one of the techniques in the portfolio of time consuming ones. Since the distribution is dependent on the correlation parameter you would need to run a MC each time you price a tranche. Calculating the implied correlation would take forever.

jenniferlwj · August 26th, 2005, 4:00 pm

What should be the possible values for those bucket size? Any suggestions?I coded for Hull White bucket model and am still debugging. Should the CDO result highly dependent on size of bucket? (in my current 'wrong' implementation, that's true.)Thanks.

jenniferlwj · August 26th, 2005, 6:40 pm

nyone help me verify the probability of loss in bucket k with each coupon date?Parameters: 100 names with ech notional 100, homogeneous, Recovery 0.4, lamda 0.03, cor 0.3, quartly resets, 5 year, tranch lower: 3%, upper: 14%, r = 5%, buckets: K = 19, hence totally 20 equal buckets, (0., b0), ...(b(k-1), b(k)). I can't get correct results, and observe that the expected loss (ti) can be less than the expected loss (t(i-1)), which is wrong. I'll greatly appreciate it if anyone can verify the probability file I attached. I use Hull white bucket approach.

Firebird · August 26th, 2005, 7:53 pm

who would like kindly forward Anderson, Sidenius and Basu's paper to me? My email is huang002@bama.ua.edu. Thank you ahead.

jenniferlwj · August 26th, 2005, 9:03 pm

In HW bucket approach, why do we need estimate the prob that a loss equal to mid bucket between T1 and T2 instead of just estimating the prob ... by time T2?I also refer ASB's paper. I use formula (16) in ASB (after getting rid of spread) to price CDO. There, the expected loss over coupon interval (T_i-1, T_i) is (e_i - e_i-1), where e_i indicates the expected loss absorbed by the tranch up to time T_i. Hence what I'm really interested is evaluating e_i; and it turns out to calculate P(mid_bucket;T_i), which is similar to P(l;T_i) in (17). This probability is the prob that discrete loss equal to mid point of a bucket by time T_i. (note, not (T_i - T_i-1)?)Anyone who implements HW bucket may take a look at my calculation in file. I guess I'm wrong since I don't use the formula HW gives specifically in Page 12 just before section IV. Thanks.

jenniferlwj · August 31st, 2005, 2:30 pm

Anyone implemented Bucket model? My result from HW bucket is totally different with Monte Carlo because default leg payment is too small. Anyone may clearly explain the DL, PL calculation?Thanks.