Credit spreads to survival probabilities

schizoidman · April 15th, 2006, 11:54 pm

Hi,I've been trying to manually calculate the default probabilties on the Bloomberg CDSW screen using the JP Morgan model. It seems that the Morgan model uses a hazard-rate function of credit spreads to analytically compute the default probabilities rather than solve for them. I've managed to come close, but it's still not exactly the same as Bloomberg. I'm attaching a spreadsheet, and I was wondering if someone could give me some pointers.Going by the screenshot, it seems that the BGN rate curve is also some sort of input into the probability calculations. I was wondering if this could be my missing piece.Thanks in advance.Schiz

schizoidman · April 17th, 2006, 7:30 pm

Let's see if this works...I can match Bloomberg close for 40% recovery, act/360, qtr payments and very closely for 25% recovery, act/365, sa payments.

Rez · April 17th, 2006, 7:37 pm

you might want to zip it firstK.

cosmologist · April 21st, 2006, 3:59 am

Can I have the JP morgan paper,please.thanks

Satriani · April 21st, 2006, 1:40 pm

shizoidman thanks a lot!!!! a perfect excel I think!! can anyone also send the paper please!!!

Wibble · April 21st, 2006, 1:43 pm

The paper (if it's the one i'm thinking of) is on a previous thread, from memory it involved matching BBGs CDSW

AlanB · April 21st, 2006, 4:43 pm

QuoteOriginally posted by: schizoidmanLet's see if this works...I can match Bloomberg close for 40% recovery, act/360, qtr payments and very closely for 25% recovery, act/365, sa payments.Maybe what Bloomberg does is DfltProb(i) = 1-Exp[-Sprd(i) * t(i) /{ (1 - R(i)}]

schizoidman · April 21st, 2006, 4:56 pm

Hi,Actually I wasn't working with the JPM paper in mind, but just trying to work backwards by matching Excel with Bloomberg. If someone does find the paper, please post it on File Share.If I remember correctly, I had read a Lehman paper that had said that survival probs are not analytically calculated, but rare solved using the single-name CDS pricer. However, it does look like Bloomberg calculates an analytical solution.

Tunito · April 21st, 2006, 5:33 pm

My dearest cosmologist,QuoteOriginally posted by: cosmologistCan I have the JP morgan paper,please.thanksI would like to read that paper also. Could you do me a favor to post it on the forum?Still, I am chasing after you, my pal!Tunito the Maverick

NoelWatson · May 10th, 2006, 3:26 pm

schizoidman,I've had a quick look at this and I think there are two things that are missing1). Interest rates definitely affect the default prob2). Changing a spread affects all subsequent spreads i.e if you change a 3 year spread, the default prob for 5 year and up change.RegardsNoel

Sgaragnaus · May 11th, 2006, 8:37 am

schizoidman,i think you should use a time dependent hazard rate function in order to try to replicate the Bloomberg results.If you choose a piecewise constant hazard rate the survival probability will be S(t) = exp(-\sum_i {h_i * Dt_i})where h_i is the constant hazard rate value for the i-th interval and Dt_i = t_i - t_i-1 is the i_th time interval in wich the hazard rate is constant (the last interval in the summation is Dt_n = t - t_n-1).You can think at t_i as the i-th CDS maturity, so that if you have k CDS market spreads you will have k time intervals (t_0 is the valuation date). With a piecewise constant hazard rate you have to use a bootstapping procedure starting from the shortest CDS maturity and moving to the longer ones step by step.In each step you have to solve for the h_i numerically (keeping h_1,...,h_i-1 constant), by imposing the equivalence of the premium leg and the default leg for each market CDS.

allenishands · May 15th, 2006, 7:57 am

How about this.Here is my model which calculates default probabilities from CDS spreads.The default probabilities are also affected by recovery rate and interest rate.

Oleg · May 15th, 2006, 8:48 am

Hi allenishands,you mentioned that default probabilities are affected by interest rate.Assuming the DP is unchanged, can one estimate how the change of interest rate affects the spread?

allenishands · May 15th, 2006, 9:19 am

Hi Oleq.Yes, it is possible to do that in the formula of my model.But I didn't do that since that is not my main point of my thesis.

HPBarone · May 15th, 2006, 3:29 pm

Hello Allenishands,I tried to get the same results as CDSW some time ago.I put my results in your spreadsheet.Does your computation take long time ?Would it be possible to read your thesis ?Thank you.HPB