Bootstrapping SurvivalProb from CDS spreads

amitk · January 7th, 2008, 1:00 pm

Hi I have constructed a spreadsheet for bootstrapping SurvivalProbability from CDS spreads http://www.quantcode.com/modules/docman ... _dir=17Now I am trying to write VBA code for the same. However, how do I call SOLVER from VB Subroutine?any help ??

Balmung · January 8th, 2008, 2:01 pm

You do not necessarily need a solver for that.Set Premium_Leg=Protection_Leg with N=1 and you obtain SurvivalProb(1) using simple algebra, since SurvivalProb(0)=1. Continue with N=2 to obtain SurvivalProb(2) and so on ...Regards

gkmitov · January 8th, 2008, 8:13 pm

QuoteOriginally posted by: BalmungYou do not necessarily need a solver for that.Set Premium_Leg=Protection_Leg with N=1 and you obtain SurvivalProb(1) using simple algebra, since SurvivalProb(0)=1. Continue with N=2 to obtain SurvivalProb(2) and so on ...RegardsAnd you should also make an assumption about survival probability time structure!

pandrea · January 16th, 2008, 3:37 pm

Hi guys,I had a look at your spreadsheet.Basically, if you want extract hazard rate from CDS spread using a deterministic environment, one issue could be the risk of obtaining negative hazard rate during the iterative process.does anyone kno how to solve the issue related to negative hazard rate?Do you have to use a numerical method?what do you think about this paper "Bootstrapping default probability from CDS spread".AndreaJunior memberThank you all

rickyzhang · September 12th, 2008, 1:59 pm

The reason of bootstrapping negative hazard rate is because the CDS spread curve is inverted or humped. This usually occurs in the distressed corporate bond or non-investment graded bond.I don't we can solve it by using different numerical methods.I guess there should be another kind of pricing method for negative hazard rate.

pandrea · September 12th, 2008, 2:02 pm

Hi rickyzhang,thank you for your reply.Do you have any suggestion about which numerical methods to be use it?RegardsAndrea

rickyzhang · September 12th, 2008, 5:24 pm

I mean it is not numerical method that causes negative hazard rate. The implied hazard rate is negative if the CDS spread curve is inverted.I am stuck in my work because of negative hazard rate. I'm still looking for solution to it.I'm reading the paper about pricing CDS with underlying bond is distressed. But so far I have no clues. FYI: http://www.imf.org/external/pubs/ft/wp/2006/wp06254.pdf

freddiemac · September 13th, 2008, 1:33 pm

Hi! I am not an expert on this but hope I can help you out. The hazard rates shall NOT be negative just because you have an inverted CDS curve. If you get negative hazard rates then you have something wrong in your model or the CDS prices that your are using are flawed. The latter happens quite often if you use data from eg Bloomberg. The 5y Cds prices are updated often but eg 1y may be lagging alot. again you dont need a different model for stressed names, it is something in your model or data that is wrong. can you please give some more info on how your are trying ti implement the model and maybe i can help you out?to use the solver in vba u cannot simply record a macro using the solver. you need to have reference to the solver in vba library. see this link:http://peltiertech.com/Excel/SolverVBA.html#Solver1hth and give some more info on what your problem with the neg hazard rates is. i just implemented an excel spreadsheet using vba solver for cds pricing and calculating hazard rates. i can give it to you but i have it at work and i am home with a cold now. boooring!

rickyzhang · September 14th, 2008, 4:57 pm

Let me briefly describe my problem.Given the constant recovery rate 40%, the following inverted CDS curve:Tenor (Years) CDS spreads (in BPS)1 3202 573 1324 1395 1466 1507 154Please demonstrate how to bootstrap a non-negative hazard rate.My algorithm is from Lehman Brother's paper that the hazard rate makes the equation "Protection Leg=Premium Leg (no accrual premium)" at different maturity (from i=1 to 7). However, the paper doesn't provide method to solve it.Thanks for your help.paper

freddiemac · September 14th, 2008, 6:56 pm

Hi! I have read another paper by Lehman where they use a simple trick for avoiding negative hazard rates. I have it at my job but I will not be back there until thursday. I guess it is a paper about BCDS (bond implied cds if you want to search the web for it). it is nothing fancy I guess you can just make any adjustment since you are really violating the data. However that CDS curve that you posted looks downright wrong. Thus it is not necessearly your model that is incorrect it may be the prices. look in the cds paper that you posted, they discuss that, but i guess u know that. so i guess u have to ask yourself if u really want to fit the entire curve including the 2y point (it looks wrong). perhaps u do need 2 fit the entire curve then u need some trick to avoid neg haz rates. sorry but i am home sick so i am just babbeling.. anyway i will look for the paper on thursday. if you are desperate try searching for it in the lehman quant credit quaterly. i havent been much help..good luck 2 u!

rickyzhang · September 14th, 2008, 8:28 pm

Take care, dude!!!where are you? It is very hot in North Carolina. If possible, could you tell me the keyword to find out the paper you mentioned?My boss may fire me if I can't get it done ASAP.

Yossarian22 · September 15th, 2008, 8:06 pm

We let the PNDi ( Probability of Not Defaulting) = 1 at time zero. now at time t<T PNDi has to be less than 1. All you do is take the absolute value of the change in PND from time step i and i+1. I have done this in a spread sheet last year, but it basically is just taking the equation for the spread Sn in the JPM handout attached in this thread and backing out PNDi for each i. If you need further help I can go look for the spreadsheet. Y

Yossarian22 · September 15th, 2008, 8:08 pm

Freddie are you talking about the paper by pugachevsky?

rickyzhang · September 15th, 2008, 11:07 pm

PND= survival probability. Based on what you said, it is non-increasing series. However, in the case of inverted CDS spread, it is not non-increasing. You'd better try the CDS spread data I listedToday I met a European quant. He told me either treat it as zero or let the user define it.I will let it go unless Frediemac give me a further instruction.

Panoramix · September 16th, 2008, 7:29 am

Why don't you use both methods?In the paper you posted, you can use the method which produces negative hazard rates, just in order to verify if arbitrages are possible, and then try to find out another model which produces positive ones.Negative hazard rates do not necessarily mean that it is wrong.