If interpretability is sufficiently important, you could straight-up search for mathematical formulae.
My SymReg library pops to mind. I'm thinking of rewriting it in multithreaded Julia this holiday season.
My SymReg library pops to mind. I'm thinking of rewriting it in multithreaded Julia this holiday season.
It is indeed of limited use, since often I can spot the relationship visually. And once I get the general equation I can easily transform the data to get a linear regression.
And closed-form equations are themselves almost always simplified or abstracted models derived from real-world observations.
Which is why actual option prices have the "smile", with tail prices being higher than the model would predict (because traders know that the model underestimates tail risk, and generally have a good sense of how far it underestimates it, because the model is fairly transparent).
Because B-S is closed form, you can run it backwards, to convert actual prices to an implied volatility.
Which is also known to be wrong, because historical standard deviations of returns are only somewhat predictive of future observed returns.
As one person put it, Black-Scholes is the wrong model, into which you put the wrong data, to get the right answer.