I calculated values for put options (european and american) using the implicit finite difference method and compared them to black/scholes values.
The values for american put options are higher than the values for european put options (BS and finite differences), which is in line with theory.
I applied the same code to call options, setting the lower boundary to 0 and the upper boundary to S(max)-K. The values using finite differences for american and european options are roughly the same. The BS Value lies considerably above both values. I expected the values of the european options to be almost the same and the american option value to exceed both.
My code is more or less based on the following source (for put options, for call options i simply changed the payoffs to max(S-K,0) and changed the boundary conditions (see above).
Does anybody have an idea? I changed the grid size, which didn't change much.
Thank you in advance!