I found some very interesting (promo?) slides from SocieteGenerale discussing WHY the Libor Market Model LMM [aka BGM/J, an instance of HJM] has become so popular, despite its significant imperfections.
But are we fooling ourselves that we can still put “the wrong number in the wrong formula to get the right price”?
I think they miss the point, basically you need some parameters to make a good model fit the environment [to paraphrase Dermans definition of useful ‘model’ is that it allows you to price something from other, somehow related, market observables]. Sure, you need several parameters to get enough flexibility to calibrate to the market.
But thats still not it, because if I give you a 15th order polynomial, you can make it fit anything… the model should reflect an understanding of Nature – it should encode some principles about markets. I think even heuristic physics models [think Bohr atom , or liquid drop nucleus] actually do have some physical basis… a valid analogy… so that the parameters you supply, do have some meaning, they are not pure curve fitting.
So… do HJM / BGM/J have too many parameters and too much curve-fitting ‘black magic’?
Maybe its time to throw away Brownian motion, but keep martingales, use a Levy process with a spectrum that matches reality, keep the ideas of no-arbitrage and see where it leads… and it may lead to a much simpler model [very unlikely to be analytically solvable, but probably evaluates numerically much more quickly than what we have now.] and which really captures the intuition of whats going on with the feedback between varying interest rates and varying asset value.
Theres always room for improvement right?
Heres the original paper on BGM – “The Market Model of Interest Rate Dynamics” [the only pdf I could find online, wikipedia surprisingly doesn’t link to it].