Agree completely on 1. but not sure on 2. and 4. - I think if you're using Python and need performance then you will be using Numpy etc - would be interested to hear if there are instances where this doesn't work.
numpy is great for vectorizable calculations, but many calcs (particularly for long-term life contingent risks, i.e. reserves), are not vectorizable except in the most simplistic cases.
Numba can usually speed up non-vectorizable things by JIT compiling and potentially parallelizing.
I mean, in an ideal world you'd use Julia or a Cython extension, but if you already have something in Python/numpy, numba only requires you add a decorator to your function and it gets jitted.
Thanks - sorry I'm struggling a bit - wouldn't they be vectorizable across the portfolio or across scenario for stochastic calculations. Maybe it's because of different backgrounds (mine in UK) but I'm can't recall seeing the deeply nested function calls that you're alluding to.
Think about the calculation of an insurance product with a Fund Value. Everything is forward recursive with respect to time. Been a while, so I might butcher some of this. It is likely that you'll want a 30 year projection, so you'll call fundValue(30 * 12)
fundValue(t+1) = if t > 0 fundValue(t) - charges(t) + intCred(t) else initialPrem
That code looks very familiar! I see what you mean now. I don't think I've ever seen this implemented recursively though - can certainly see how this would end up being problematic if you tried to do this in Python!
ps Thanks so much for taking the time to set this out.
pps I've been working on something that implements a highly optimised version of this style of calculation - with a DSL to describe the calcs - can do 30 year cashflow projection for 1m contracts in about 1 min on quad core laptop. UK focus initially but might have wider application?
