Cuchulainn wrote:The first order problem with models that lack a relatively simple mapping from state variables to discount factors arises when you have a short dated option on a long dated bond or swap.
What kinds of problem? model, numerical, time scales?(?)
To take an example that I will admit bordering on the silly - let's say you want to value a three month option on a futures contract where the underlying is a set of 25-30 year coupon bonds, and where you want to consistently value the underlying bonds, the futures contract (via a cheapest-to-deliver embedded option) and the option contract. In a classic lognormal short rate model you need to build a 30-year lattice to value the bonds, but you would also like a relatively fine spatial resolution at the three month point to get reasonable precision in the option pricing part. I am not saying you can't do it, just that it is a lot more demanding than building a three month lattice and determining the terminal bond values (and thus futures price and option payoff) analytically, as e.g. in a Gaussian model.