Hi All,Most of models used to price and hedge credit derivatives products are very dangerous especially the copula approach..Because the prices used by theses models are not based on a hedged strategies but on the average of some scenarios (like what insurance people do).. 1) In general people hedge only the spreads variations when hedging products like CDO's but by pricing with copula functions they assume in general deterministic spreads..2) The copula function doesn't conserve the Markov property: The price in a future date of a multi underlying product using any copula depends on the realization of the spreads between today and this future! Which is in contradiction with how people price these products today (the only consider today's market parameters). I think that credit modelling is more closer than insurance approach rather than to quantitative finance based on hedging..What do you think?

I'd agree that copulas are not the 'all singing and dancing' solution, but they serve a purpose.To apply hedge based pricing you need to have sufficiently available (at a cost) hedge instruments. Some stuff in the structured credit space is priced using hedge-based principles. Also, do not forget, that someone somewhere might hold unhedged risks and for them the insurance approach might be quite appropriate.Not being Markovian is in itself neither good nor bad, inconsistencies usually arise when there isn't enough to 'go by the book'

yassin2: can you please explain why copula functions don't conserve the Markov property?does that mean they introduce some sort of dependence on history?i am confused, but then again i am a trader not a quant...

In general, the statement that stationary Markov chains can't be constructed from copulas is wrong, but not all copulas allow for such a construction. They have to meet certain conditions.If I recall correctly, you can construct Markov chains based on Archmidean and Gaussian copulas.

When you price a FTD (Let's say with maturity 5 years 2005-2010) today, you take into account the today's market spreads and you input a correlation parameter (copula parameter)..If you write the price of this FTD in one year (so you have a residual maturity of 4 years 2006-2010) it will depend on the spreads between 2005 and 2006! This is not natural since in 2006 you will consider only the spreads at this date. The only copula which doesn't have this property is the independent copula ..Most of banks price cdo's with using copulas (Gaussian, student or Marshall olkin) and they suppose that suppose that spreads are determenistic..The problem is : even if during the life of the product the spreads remain contants the P&L using delta hedging will not be what you you expect because you have an additional "theta" coming from the fact that most of copulas don’t conserve the markov property (except the Independent copula)..

Zed,How do you that ?

there is something about the how to in 'Investigating Dynamic Dependence Using Copulae' by E. Bouye et al.

We are not talking about the same thing!When i say that the copula doesn't conserve the markov property that mean that prices at a future date depend on all spreads between today and this future date and not only on the spreads at this future date ..

I'm not sure I can follow you, if you calibrate your intensity functions/copulas today, you will not look at just todays spreads, but the spread history, as you would in 2006. I'm probably misundertstanding you...

If you price with independent copula the price will depend only on the spreads in 2006..In 2006 you have a FTD with maturity 4years and if you price this FTD-4Y you should only use the information available in 2006 as you do today..Am i clear ?