I think the problems go right back fundamentally to David Hume as people have discussed time and time again on these forums. Basically quant finance is not a science, just a more numerical part of economics which has got itself a bit stuck in a rut and forgotten to be widely read about economics.Paul's point about Hooke's law and some such parameter calibration in finance is not the problem in and of itself, it is just a very nice illustration of why all financial models are deeply flawed philosophically. One simply cannot defend calibration because it is logically inconsistent as Paul points out - you have disproved your own model's parameters by having to recalibrate it. If you have to do this under all market conditions without reliable known boundaries of applicability then you have disproved your model.However, does it matter if all quant finance is philosophically flawed? What is the problem we are trying to solve? Hooke's Law (although perhaps not really a Law any more, not like conservation of energy etc) attempted to solve the problem of the observed relationship between the extension of the spring and the mass on the end. Hence it is a scientific question with easily reproducible experiments with which to falsify the "Law" within the use cases defined as part of the "Law" in and of itself. In finance, as the original poster poses by the question, we are actually not trying to write a "Law" which can be testable in and of itself. Actually, our boss has told us that a client wishes to enter into some kind of crazy OTC exotic contract and we wish to fill the client's order whilst minimising the bank's risk, then take them out to the rugby and get drunk together and pat each other on the back. We hope that following on from this deal that any / either / all the following things may or may not be true in order of importance 0.) We made our boss happy and we can always leave or get bailed out if it all goes horribly wrong1.) We made a fat margin and fooled the client into being happy2.) The client is good for the cash if it all goes wrong; and they are a good sport / laugh if they lose their money / we go out drinking3.) Our model was vaguely something which with good luck will turn out not to be horribly wrong in the time period of the deal4.) We manage to do some kind of combination of static and dynamic hedging in liquid markets which remain open, with entities which are good for their money, or they get bailed out if it all goes horribly wrong5.) If we got it wrong, everyone else got it wrong, or there is some kind of fall guy, or we are all the fall guy and therefore don?t feel bad if we all have to pitch in foraging for berries together in the central reservation of the M25.Here is where I am really cynical about quant finance, and so best to pose a positive question: Paul et al, if you don't like calibration (or implying parameters from the market) what do you suggest? Some form of eigenvector analysis to find principal components instead of blind Gauss distribution models with no proof of central limit? Some kind of trained classifier, for example used in computer vision? I noticed talk of Fisher's Linear Discriminant Analysis elsewhere (was it referring to Fisher describing the separation between distributions of two classes to be the ratio of the variance of the classes?) ...I think it needs to start with economic thinking, not mathematical: what I would like to see is some mathematical models for derivatives contract valuations based on more than just Gene Fama, taking Keynes and others into account explicitly in the model's original assumptions?. But then that is another story ?
Last edited by TitanPartners
on May 8th, 2011, 10:00 pm, edited 1 time in total.