I have been reading about natural filtrations, and I think I have a good grasp of them. However, I also found out that natural filtrations are just one type of filtration in general. Now I am not able to imagine a filtration other than a natural filtration which would serve a purpose.
So the question is, how does a filtration generalize the idea of a natural filtration, and in particular, where would I use a filtration which is not a natural filtration.
(For context, I am studying valuation of derivative contracts, and they are obviously riddled with natural filtrations.)