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helgus1
Topic Author
Posts: 15
Joined: April 25th, 2005, 11:41 am

### How to get default intensity structure from CDS prices?

Hi EveryoneCould Enybody help me how to obtain a credit curve (default intensities) from Credit Default Swap prices? I would be grateful for any reference or explanation.

Aaron
Posts: 6433
Joined: July 23rd, 2001, 3:46 pm

### How to get default intensity structure from CDS prices?

The most difficult part is figuring out the implied recovery rate. Once you have that, it's simple to get the implied default probability (the actual default probability cannot be inferred from market prices).Suppose the premium for the first period is X and the recovery rate is R. A one-period protection buyer pays X if there is no default and gets 1-R if there is. That's a fair bet if the probability of default is X/[X+1-R]. Once you know the one-period probability of default you can use a two-period CDS to estimate the probability of default in the second period, and so on.Of course, you may not have good quotes for all periods, so you may have to interpolate.
Last edited by Aaron on April 26th, 2005, 10:00 pm, edited 1 time in total.

helgus1
Topic Author
Posts: 15
Joined: April 25th, 2005, 11:41 am

### How to get default intensity structure from CDS prices?

Thanks Aaronbut now I'm confused. I want to understand work of Umberto Cherubini "Pricing Swap Credit Risk with Copulas". There he writes: "...we assume to observe the term structure of default intensities and take the worst case scenario concerning the loss given default figure Lgd=1 ", that is Recovery Rate zero, and further "...we use default intensity structure bootstrapped from CDS prices..."With your proposition and assumption of Lgd=1 probability of default equals 1 in first period. I know that I'm missing something, but don't know what. Maybe some underlying assumptions or bootstrapp method?

Aaron
Posts: 6433
Joined: July 23rd, 2001, 3:46 pm

### How to get default intensity structure from CDS prices?

No, if the cost of a one-period CDS is 100 basis points per year, the implied probability of default in the first year is .01/1.01 = 0.0099. I think the confusion is I use R = recovery rate = 1 - loss given default.

baydar
Posts: 18
Joined: November 28th, 2004, 5:45 pm

### How to get default intensity structure from CDS prices?

stripping the risk-neutral PDs out from the market CDS spreads is a better method relative to have them from corporate bond data, since especially 5Y CDS is very liquid in market so the PDs do not include the "liqudity risk".the procedure is mainly called "bootstrapping" and a model-dependent bootstrapping methodology would be:assume you have market CDS spreads with 1 3 5 7 10 Year maturities, the constant recovery rate, the yield curve for discount factors...assume you have a stepwise constant hazard rate, i,e, \lambda_1 if 0 < t < 1 Y, \lambda_2 if 1<t<3 Y....and so on. then get a simple CDS pricing formula and with a JT95 type credit risk model setting assume that PD(0,t)= 1- (exp(-\int_0^t \lambda(s)ds )) -> since we assume the intensity rate is constant,it is easy to find the \lambda which are making the value of the CDS=0 at valuation date with a numerical algorithm(i.e fzero(...) in Matlab).this is an iterative method, i.e. we use the 1Y CDS market spread to find lambda_1,using lambda_1 and 3Y CDS market spread we calculate lambda_2 and so on....

hateeque
Posts: 21
Joined: October 7th, 2004, 2:43 pm

### How to get default intensity structure from CDS prices?

Can you show us the recursive (bootstrapping algorithm) for computing probability of default at longer tenors?

warwick006
Posts: 6
Joined: July 10th, 2007, 12:54 pm

### How to get default intensity structure from CDS prices?

I am dealing with more or less the same problem..I am workin on my dissertation on credit risk modelling and would like to move soon on default dependency modelling. However, I need first to extract implied probabilities and wanted to try to do it for single names..can u tell me in particular what risk-free to use? thanks

amitk
Posts: 18
Joined: March 16th, 2007, 10:19 am

### How to get default intensity structure from CDS prices?

I had worked out a xls for bootstrapping Survival Prob from CSD spreads(without VBA). It is based on Lehman Bros paper. Listed here..http://www.quantcode.com/modules/mydown ... &lid=412It currently handles 7 year tenor at maximumhope it helps

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