Let's say I have an asset that has returns that are perfectly normally distributed. Let's say there are American Options on this asset. How does a plain vanilla BS model mis-price the American option?Assuming all inputs are constant, would:-BS model always show a lower price than the American option? This makes intuitive sense as American options allow for early exercise. Would this under-pricing hold true for both calls and puts and at some sort of constant rate for all strikes?The reason I'm asking is because I'm trying to create a spreadsheet that prices spreads on American options. The model doesn't have to be pinpoint accurate, but I need to see what happens to the spread as the different inputs (price/vol/time) change. Since credit/debit spreads involve going long/short a put or call of different strikes, would the underpricing cancel out?Can I use a vanilla BS model to price spreads on American options accurately?

if you just need it to be very, but not always precisely, accurate (to the extent that BS produces an "accurate" price): if the stock pays a dividend, calls may occasionally be mis-priced and puts will be fine for your purposes; if no div, you're fine. just figure out/look up early exercise conditions to see when they matter - if they don't matter, european value will be the same as american value.

QuoteOriginally posted by: sladnerif you just need it to be very, but not always precisely, accurate (to the extent that BS produces an "accurate" price): if the stock pays a dividend, calls may occasionally be mis-priced and puts will be fine for your purposes; if no div, you're fine. just figure out/look up early exercise conditions to see when they matter - if they don't matter, european value will be the same as american value.American put > European put even if divs are zero.

i know, but for what he's doing the difference is going to be negligible, especially in zero rate environment...(why i said "for your purposes")

I may be wrong but if he is working on options on futures with rate around 0 he will see no difference between Black for European and American value.Even with higher interest rate if he focus on OTM options which is what is on the market he will see no difference.

it doesn't matter what the underlying thing is, if there are no circumstances under which one would exercise early, american = european

For American calls use Black's approximation which uses 2 evaluations of the BS formula