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numbersix, I think you might be on to something. I find that most report median spreads, presumably because the a few distressed issues can wreck arithmetic averages. I take averages for only issues with spreads below 2000 bps above libor. This generates an unfortunate dichotomy in that I generate nonparametric spread expectations *assuming* no distressed, and this exception is more material the higher the spread. In sum, I see a dilemma: use all spreads, and get spreads that are on average too high, ignore distressed issues and understate the true expected spread. It is as though once a company enters a distressed regime its price (spread) uses a different pricing function, but one can't reason backward to incorporate this probability in its current price--its current state is either distressed or nondistressed, and one reasons backward only using the current regime status. Further, the arbitrary definition of the distressed exclusion rule affects the averages materially.By grade, using data from 10/12/01 using about 1000 US nonfinancial issuers, I get the following spreads & probability of being distressed (defined as having a spread>2000 bps):rating % distressed spread to libor (bps)AAA 0.0% 38AA1 0.0% 41AA2 0.0% 45AA3 0.0% 51A1 0.0% 84A2 0.0% 114A3 0.0% 136BBB1 0.0% 162BBB2 0.0% 211BBB3 0.0% 306BB1 0.0% 457BB2 2.6% 536BB3 1.3% 633B1 11.4% 752B2 19.6% 974B3 29.4% 1100CCC1 56.8% CCC2 66.7% CCC3 75.0% CC 83.3%

In a word, we are making it so that a "distress PDE" may be solved on the side of the regular one >>Elie, since we’ve talked about Jump-Diffusion before, how about using a more general Jump-Diffusion model, i.e. one that allows for a life after jump (crash) … I mentioned this before in the “Volatility Smile” thread, but there is a Steven Kou article on this …

Is 'default' more likely at times when the company has coupons, dividends or other cashflows to pay out? P

Reza, this is exactly what the "distress PDE," that we solve in parallel to the regular one, is supposed to govern: a life after jump, or crash, or default... (again, any ideas are welcome)Paul, supposing default has occurred and there is life in this limbo, would that mean the CB is not risky anymore? (The company has no coupons, dividends or cash flows to pay out any longer, just the "default settlement"). In other words, should we use a risk-free discounting in the "distress PDE" ?

numbersix, I guess it depends on what the company is doing in this distressed state. Still operating, selling off its assets,... I am fortunate never have personally been bankrupt so I don't know what the procedure is! (Of course, that means I am too conservative a businessman!) I am imagine that there's a lot of legal s**t to sort out.But I wanted to know how the outside world gets to know about problems within the company (whether in a distressed state or not). Often (usually?) it's at the time of earnings announcements or, I imagine, when they have to pay out a lot of cash. So I would expect the probability of 'default' or ratings transition or whatever to have a delta function at such times. P

Elie, in terms of “ideas” I would again recommend (for instance) the article by Steven Kou (I think it's on his web-site) “A Jump Diffusion Model for Option Pricing with there properties: leptokurtic feature, volatility smile and analytical tractability” … the issue is the choice of the jump-size functional form and also the calibration. If we consider (like him) an exponential jump size and try to calibrate its parameters to distressed bonds perhaps it would work? of course there are other possible choices.This way we would also link the volatility smile (and fat tails) to credit events which would be interesting …