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Hi, I am trying to figure out why using the transformation x= Ln(S) is computationally more efficient when using finite difference methods . Can anyone share with me why we use this transformation ? One reason that I can think of is that after the transformation, the differential equation will have a constant drift and variance and will cut down the computation time for the finite difference method. Anyone can help ? Thank you.

Finite difference methods essentially solve the heat equation - when simulating x=logS. As the heat equation is the simplest equation of evolution, these methods have better properties in this case - uniform grid, stability and convergence, etc.