# FX Option pricing on Forward vs. Spot

In a GBM world with riskless domestic and foreign interest rates, what would be the correct model for a FX plain vanilla option given the statement that this option is priced on the forward? I guess it would be the Garman Kohlhagen model or the Black (76) model but I'm a bit confused between the two in the context of pricing on spot vs. pricing on forward. I would appreciate an answer that scetches the main differences.

• Black76 formula uses "F" and GK uses "S", but they are the same when you make the substitution $F \leftrightarrow S e^{(r-q)T}$ – Alex C Jan 26 '17 at 23:34
• @Alex C, that's what I was thinking as well. I just didn't believe it;) For the sake of clarity, pricing on forward or spot is a matter of convinience depending on the inputs used, right? – Tim Jan 27 '17 at 8:55
• Yes, I find that one or the other is more convenient in a given situation. For example if it is difficult to know r and q I prefer to work in terms of $F$ rather than $S$. – Alex C Jan 28 '17 at 4:39
• @Alex C, thx, if you could write up a short answer, also for the reference to others, I can accept this. For me it was really a matter of confusion about the mentioned statements. – Tim Jan 28 '17 at 10:19
• @Alex C, I posted a follow up question, you may have a quick look. – Tim Jan 28 '17 at 11:26

The Black76 formula uses "F" (the forward price) and Garman-Kohlhagen uses "S" (the spot price), but they are the same formula when you make the substitution $F ↔ Se^{(r−q)T}$