The sigmoidal functional crops in a number of places
https://onlinelibrary.wiley.com/doi/epd ... wilm.10366
Here (Paul W's brainchild) we use it to model volatility with memory.
Another use is choosing nice and smooth activation functions (some are more equal than others). and here is one case for Heston. The smoother the a.f. the better the convergence, especially if you want to compute greeks. It could be competitive.
https://www.datasim.nl/application/file ... 423101.pdf
Smooth functions that approximate functions with kinks would be a boon. The whole issue of which a.f. is best seems to be an open issue in ML, which is very much in the 'try it and see what happens' kind of mode in general.
// I am having trouble relating it to call payoff; is it a smoother around K?