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seen Jun 27 at 17:23

Just this guy, you know?

comment Black-Scholes No Dividends assumption
For American-style options that is incorrect. The price will differ depending on how you "get to" the forward price. That is, you will end up with a different price for an option depending on your dividend assumption even if the forward is the same.
comment Discrete-time model: stock dynamics
Fur currencies, keep in mind that you don't have complete freedom --- if you specify EUR-USD and USD-JPY dynamics, then the EUR-JPY dynamics are fixed... (If you specify all currencies against some fixed given currency, say XXX-USD for all other currencies XXX you avoid this problem, but there are other annoyances with this approach, this simplest being variation in quoting conventions for various currencies, e.g. EUR-USD vs. USD-JPY.)
comment Longstaff Schwartz method
you're much more likely to get a response if you clean up the code, make it look readable, etc. (and that may help you find your bug even).
comment Methods for pricing options
I don't really understand the question. To my mind, the question of which model you use (Black-Scholes / Bachelier / local-volatility / Hull-White / etc.) is orthogonal to the numeric technique you use to implement (solve) the pricing (analytic formula / Monte-Carlo / *nomial tree / finite-difference (pde) / etc.)