Does anyone have a model that computes the probability of default from from a CDS curve? Basically, I am trying to recreate the 'Defult Prob' field in CDSW on Bloomberg. The inputs would be the interest rates (swap curve) and the CDS spreads.Thanks in advance!

read the jpm paper par credit default swap spread approximation which has been posted on numerous occaisions

amg519 - send me your email address and I'll send you a spreadsheet for bootstrapping CDS.

http://www.wilmott.com/messageview.cfm? ... adid=57636

It is quite curious to read introduction of the notice JPM "Par Credit Default Swap Spread Approximation from Default Probabilities ". Purpose: There have been considerable client inquiries on how default probabilities are calculated from credit default swap spreads using our pricing analytic1. This is a quantitative process that is not easy to explain intuitively. As such, rather than explain the calculation of default probabilities from credit default swap spreads, this paper focuses on the reverse – approximating par credit default swap spreads from default probabilities.It sounds like follows. It is not easy explain intuitively how to calculate the root of the 17 power. Rather than explain the calculation the paper focuses on the reverse how to raise the number in 17 power.The problems that they are asked and the problem that they presented in the paper are obviously different.Besides it is not clear the next issue used for valuation of the fee leg : the numbers $PND_{i}$ are multiplied by the $\Delta _{i}$This makes sense if they developed a discrete approximation of the continuous time model. In this case the value $PND_{i}$ is the density at the point t_i. On the other hand when they presented the contingent leg formula they used the difference $PND_{i} - PND_{i - 1}$ that is the probability of no default from Ti-1 to Ti . That makes sense if PND is the cumulative distribution that corresponds to their definition of the PND_i as "the No Default Probability from To to Ti". I will appreciate if somebody will explain the situation.

I can't explain the JPM paper but I was able to create an engine using Hull's paper equation (5):http://www.rotman.utoronto.ca/~hull/Dow ... per.pdfThe common assumption is piecewise-constant hazard rates (explained in Hull) which of course can be calculated using a root-finder at each step during the bootstrapping process.

Let me please to start from the beginning of the derivation of the (5):"Let q(t)δt be the risk-neutral probability of default between time t and t + δt as seen attime zero"What is the real world the probability of default between time t and t + δt as it seen attime zero?

You would probably have to look at historical default data to determine that. Here the credit default swap is valued using a risk-neutral valuation so you should use risk-neutral default probabilities. Hull gives a brief explanation of real-world vs. risk-neutral probabilities in his sixth edition p. 488.

The techniques that in finance have been named as risk neutral is known and used for more than 30 years. If one compares essence of this technique in probability theory and finance it turns out that there exist a big difference or to say more precisely the financial statement could not be justified by mathematics. I do not think that only mathematician could only to note that. For instance one can look at the begining of the paper:http://papers.ssrn.com/sol3/papers.cfm? ... 9094Bellow is a short paragraph from this paper:It is common to state that the solution of the problem (BSE) can be represented as expected value of the functional over the risk neutral process S r on the risk neutral world { Ω, F, Q }. Note that the functional is a mathematical term that covers variety payoff classes used in derivative contracts. Taking into account the change of variable represented in above equality one can see that risk neutral world does not perform the transformation of the real word security price S µ into neutralized price S r on risk neutral world. That means that commonly stated the risk neutral setting fails to perform the task of the real world transformation of the parabolic equation with the real return to the parabolic equation having risk free coefficient at the first order derivatives with respect to price variable.

I noted that some formulas in http://papers.ssrn.com/sol3/papers.cfm? ... id=1089094 related to asset swap should be changed. I will read the paper and will make needed changes soon. Sorry.

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

One thing I've never understood is the relationship between the probability of default/survival and the recovery rate. I've never much liked the JPM paper because it over complicates something rather simple that can be explained intuitively. Yet there P(D) as well as a MER paper I read are a function of a hazard rate. Yet in the same paper they go on to show graphs of the different survial curves (time on x axis, probability on y axis) for different recovery rates (curves of various convexity). Now, I've never seen a paper which relates the two in a mathematical and intuitive way. For me the cumulative P(S) = exp(-ht) where h is the hazard rate and t time. It is not a function of R so how do they plot those graphs? Am I missing something, but to me and the alegbra I know from the original paper, R is simply acts as a scalar to compute the expected loss. This will affect the ultimate spread but not the underlying probabilities. Can someone please advise?

Hi creditjedi! u r right there is no relatioship between the pd and the recovery rate. in the MER paper they calculate the different curves for a given spread. assume the spread is 100bp. you can come to that spread with different pd and different recovery rates. since the spread is a functio of both recovery rate and pd they are related for a given spread. i have replicated the MER curves in a simple spreadsheet using simple bootstrapping. if you want i can send it to u.

If you calculate with random recovery (for instance, like sidenius & anderson), you have a (indirect) link with the pd: if your state variable is low(bad economy), you should get lower recovery values. This is a empircally well observed fact and makes a lot of sense. I don't know by heart but there is also a nice regression estimate line for the recovery value. Message is: expected recovery is about 0.42 or so (historically) but they vary a lot (sigificant higher/lower in a boom/recession)