Today, derivatives pricing requires (at least) two curves - one estimation curve and one discount curve. I'd like to know how to make term structure models compatible with this two-curves-setup.Is it really necessary to extend the "classic" interest rate models like HW or LMM to the multi-curve case (i.e. to model both curves side by side in a "bigger" two-curves-model)? Or is there an easy workaround to incorporate both curves in a one-curve-model, which is good enough for most applications? For example, is the assumption of a constant basis spread between both curves too crude?Thanks in advance.

I guess whether you need a "bigger" two-curves-model depends on what model you´re currently working with. There´s a paper of Pallavicini/Tarenghi (Interest-Rate Modeling with Multiple Yield Curves, http://arxiv.org/PS_cache/arxiv/pdf/100 ... 4767v1.pdf) where they define a HJM framework based on a multi-curve approach. I didn´t have a close look on it but maybe their results provide some guidance. Mercurio (LIBOR Market Models with Stochastic Basis) discusses the extension of LMM in light of the new multi-curve environment.Given todays volatile markets a workaround based on constant basis spreads could be indeed too crude.Any other hints or experiences?

I doubt that there is a standard way of doing this. In the past people would often bake a deterministic spread assumption into the model. So, for example, take a BGM model and use that to simulate cash forwards, i.e. effectively the model then describes the forwards at which you accrue interest. Whenever you need a forward fixing, apply the spread that comes out of your curve system. So if you need 3M LIBOR, the work out the spread of yor 3M LIBOR curve to your cash curve and apply this spread on top of the BGM cash forward. Doing this is actually already quite important. Now, this is not a perfect approach of course. But there isn't an easy way to bring several curves under the same hood. What you are basically saying is that you want a term structure model that consistently models the term structure of debt not just of homogenous quality, but also heterogenously acriss different credit quality/liquidity, etc... You need a model for this. For example you need a model to model swap spreads if you want to capture the universe of interbank debt (Libor quality) and government debt (OIS, treasury quality). This is not a priori easy. And then how would you calibrate that, specifically the vol parameters?People do some stuff in long-dated FX that you might look into. Also, you could argue that you could calibrate your model twice. Once for one debt class and once for the other debt class and then start saying something aobut the spread of the debt classes. I think this would be very loose though, because here you aren't leveraging any market information that combines the two markets. So, for example if you want to leverage fed fund basisswaps or asset swaps say and then maybe also conditional asset swaps (for vols, correlations, etc...), then you need a combo model.

Re modeling the basis between Libor and treasury: isn't it simply modeling the relative credit worthiness of banks and sovereigns?

QuoteOriginally posted by: katastrofaRe modeling the basis between Libor and treasury: isn't it simply modeling the relative credit worthiness of banks and sovereigns?What about balance sheet?