Or in other words, the George Box quote:
"It has been said that "all models are wrong but some models are useful." In other words, any model is at best a useful fiction—there never was, or ever will be, an exactly normal distribution or an exact linear relationship. Nevertheless, enormous progress has been made by entertaining such fictions and using them as approximations."
"It has been said that "all models are wrong but some models are useful." In other words, any model is at best a useful fiction—there never was, or ever will be, an exactly normal distribution or an exact linear relationship. Nevertheless, enormous progress has been made by entertaining such fictions and using them as approximations."
I already did and you pointedly ignored me, so I feel like I am wasting precious bytes. But I'll humor you since I am waiting for something to finish calculating.
In general, a good model does not need to perfectly reflect reality. Instead, it is a conceptual representation that is based on a set of assumptions that can be explicitly and easily understood. The level of detail is chosen for a specific purpose, balancing fidelity against tractability. Look at other disciplines for examples of scientific models. C. elegans (aka nematode worm) has 302 neurons and yet it is a good model for how our central nervous system functions. Is it a perfect representation? By no means, but it's easy to work with and easy to understand. There are numerous examples like this, from Schwarzschild radius to Navier-Stokes PDE.
Black Scholes is a good model because it's based on an intelligent set of assumptions and is so simple. That makes it tractable, easy to fit and understand the perturbations. The models like SLV are much more complicated to fit, have free variables that required historical estimation and still don't reflect the real life dynamics.
