I promise to stop beating on rigid instrument-model-method combinations - once. It is a great idea, when models are not only approximations of reality, but game rules that make the market a kind of a fair play - like the option theory based on Black Scholes with analytic solutions (as it was by 1987 before out of the money options were constructed and traded).
But you can always destroy such constructs in even moderately complex cases. Try to apply tree methods to solve the adequate BS model to analyze barrier options - see To Tree or Not To Tree.
But let me be an abstractonaut for a little while. I believe in the speculative realism movement in philosophy (speculative materialism - Quentin Meillassoux - to be more precise). They claim (I simplified): if we do not know more about the behavior of a real phenomena than expressed in the properties of our (mathematical) models; our model IS reality.
At the other hand, we know this all to well: it is so difficult to close the gap between our calculations and real behavior. And I am not referring to systemic risk in the large and the ill-defined idea of the efficient market hypothesis (EMH).
To value instrument constructions with complex contract features by a set of models and techniques is not so easy. And I ask myself why so many financial experts still cling to (their) favorite instrument-model-method combinations and - why some, who take the most strict position have a lot of followers? Provocatively asking: the best quant is the most macho?
I am the marketer, and comparatively poor in financial engineering, modeling and numerical schemes. But I read a lot. And when, say, Andreas and myself have one of this creative-evening-(Pub)meetings it quite often happens that I propose: ".. there is this new deal type modeled by this and applying our that solver we could introduce it immediately ..."?
"I need to check", Andreas answers usually - and simulates in our orthogonally organized instrument model-method framework, prototypes a new method, ...
And this effort might result in this kind of insight: Extreme Vasicek Is Not Extreme Enough. No, we do not price simple bonds with Vasicek, but we check higher level solvers across extreme cases.
And we like it, if our approaches are challenged.
