Hi,Has anyone come across a model to evolve base correlation skew going forward (i.e. directly as opposed to via stochastic recovery)?Thanks...

What do you mean by stochastic. Evolving over time? As the classic copula style models are static.If you mean "random" correlation analagous to the recent wave of random recovery models i.e. you make correlation/recovery depedenet on the common factor. Then you are talking about random factor loading models which have been about for a long time. But I have not seen these used in the context of base correlation. The idea behind using RFL try to avoid the use base correlation.If you mean otherwise (a non-static copula model) then there is a paper"Dynamic factor models" by Ken Jackson, Alex Kreinin, and Wanhe Zhangwhich makes the factor model time dependent. I think this leaning towards a Hull & White model. Take an existing model with deterministic parameters then make them time dependent to try and improve fit. If you want to start evolving some process over time to try and model CDO then I am guessing a top-down approach is needed i.e. you apply some stochastic process to the portfolio losses. These are homogeneous models which lose all granularity of the underlying portfolio. Might be nice in theory but probably are not used in practice.

Thanks Max. Looked at the paper - probably not the angle that is of interest... Let me rephrase the question... We know that both base correlation and recovery affect the price, and from this point of view we can either make BC, recovery or both stochastic. The usual choice so far was to evolve the recovery. If we choose to evolve base correlation then a no arb condition on the BC skew must exist. I was wondering if anyone is aware of any work in this direction...

There is this paper by Sidenius that might be of interesthttp://www.jakobsidenius.com/papers/forwardcopula.pdfYou can derive arb-free conditions on the base correlation/expected loss - there is a paper by Jackson, i think, that talks about that. Have a look at defaultrisk.com.

anp31415,If you are talking about the more market standard stoachastic recovery model (like the BNP Paribas AH Model) then recovery is not evolevd over time but made dependent on the common factor!Do you want to apply some correlated stocahstic processes to both recovery and correlation? Is it not more sensible to apply some correlated stochastic processes to the unerlying spreads on the single names in the pool and the recovery.Compund correlaiton/Base correlation are just some magic numbers which relate to coupling the marginal default probailites of the underlying single names.

Also what do you mean by "no arbitrage"?Within base correlation framework you maybe able to force arbitrage-free expected loss conditions; positivity, monoticity, and concavity.But look at loss distributions, CS01s, Corr01 etc and base correlation is a long way from being arbitrage-free.

Max,One condition I would think of would be non-negativity of the loss distribution across standard tranches as well as bespoke ones, i.e. you wouldn't use a deeply inverted base correlation skew, would you?

not sure what you mean by "deeply inverted base correlation skew".but looking at standard tranches is ok if you are going to price up standard tranches. but if dealing with bespokes then you need to look at the loss distribution at tranchelet level when checking loss distribtion exhibits positve probabilities.

My 2cAs far as I understand anp31415, your idea would be to keep the existing models (since you are still talking about Base Correlation) and just postulate some diffusion (or another stochastic) process for that input parameter. I really think this is, from a fundamental point of view, a bad idea. First of all, there is a pratical problem as far as you are sticking with BC, then I guess you would have to parametrize that process differently for each tranche. How would you do that? I don't think that the tranche option market, if existent at all, is developed enough to allow you for doing it. Second and most importantly, as MaxCohen was pointing out, the real dynamics that one wants to capture is that of the spread of the underlying names. Ideally there would be a non flat off-diagonal correlation between all the underlyings. That's the way in whcih the reality is. In tranche pricing normally everything is spraeds are considered to be static, and only one correlation paramter is expected to be able to catch all the co-dependence structure between the names in the portfolio. I think these are the major gaps between the way the reality is and the way it is represented in the usual Copula (w/ or w/o stoch rec) pricing. That's also what would eventually allow for an effective hedging of the tranche itself, differently from what would be possible within the strategy you propose.

QuoteOriginally posted by: ZubFirst of all, there is a pratical problem as far as you are sticking with BC, then I guess you would have to parametrize that process differently for each tranche. How would you do that? That is the challenge. I guess what we want is to obtain the distribution of the stressed P&L due to BC but not standalone but as a "total derivative" i.e. when CR01s change as well. Also for longer horisons. So, we've got the first component, CR01s. Any ideas as to how to incorporate the {stressed} changes in base correlation as well?