Hi, need some help on a fairly easy question. and would appreciate some input from you intelligent ppl.

I’ve lent money to CP1, and i have recourse to CP2 if CP1 fails to pay.

CP1 PD is 3%, CP1 PD is 1%. What is the PD of both CPs defaulting if they are mutually exclusive?

Isn’t it just 3%*1% = 0.03%

Currently, when we look at this structure we assign the deal a PD of 1%, which is the lower of the 1% and 3%. Theoretically this probably isn’t right… .but i don’t wanna open that can of worms.

Given the way we’re currently looking at these deals… i need to make the argument that a doing a deal with CP3 with a PD of 0.3% is better than a deal with CP1 and recourse to CP2.

The LGD does not changes on the sequence of defaults. These are different companies altogether, so mutually exclusive unless there was some type of contagion in this industry.

Assume these are typically vanilla business loans, akin to a guarantee from a 3rd party to repay the loan in the event of a borrower default.

Are you suggesting in no event ever that having to honor the guarantee will impact their default probability? How can a contingent claim not matter unless the guarantor is vastly larger than the other entity

Brah - “mutually exclusive” means “both events cannot happen”. The probability is zero. That’s like asking, whats the probability of flipping a coin once and getting both heads and tails at the same time.

You may mean “independent” which is essentially the opposite of “mutually exclusive” - then yes, you can multiply the individual probabilities to get to the probability that both events happen at the same time.

Anyway, independent probability is a really bad assumption, and is the reason why companies like Washington Mutual and AIG went bankrupt. It should be really easy to argue to anyone why the conditions that make CP1 default could also default CP2 (the fact that they seem to have sold a ton of CDS, for instance). Why you hire Asian chicks if cannot do math?

The other thing to consider is that default scenarios always involve a lot of delays and legal costs. How long will it take to chase CP2 for the money, and how much paperwork and lawyers would you have to employ? My firm received some payments from Lehman Brothers this year, for instance. Even if payment is certain, it’s better to not deal with it.

This is interesting. There is a contingent claim on CP2 which is not factored into their cash flow forecast… so i guess you could be correct in saying that the PD of CP2 is greater than on a standalone basis.

What are the default probabilities for 1 and 2? What are the interest rates? What are the liquidation values in each scenario? Seems like this comes down to both your point estimates that go into the loss model as well as the distribution of those estimates