Thanks very much Igor for this second explanation. I strongly appreciate your going into the details here. Your comment that "Although I use the same notation, the process for the inverted FX rate is different and it results in a different Ito SDE where both location and scale parameters are different. I started with zero drift for the second derivation of FX process from practical point of view, knowing that the process is martingale and hence the drift is zero." This explains the points that I was misunderstanding: that while you are using the same notation, the actual real world process is different in the second Euro-side case and because it is a martingale then it has zero drift.

However I do feel that in order to avoid misunderstanding initially, it would have been good to have included these observations in the original text, so that literal minded mathematicians like myself don't get led astray.

Regards Michael

Thanks again Igor for your interesting discussion here on FX options. However in your triple Ito Process for the model B/(F P) given by ip03, you have F with zero drift. However from the first equation in the article we have that F has a drift of (r - q)*F. This changes the value of drift of B/(F P) so that instead of being (r-q+sigma^2) B[t]/(F[t] P[t]), it is now reduced to sigma^2 B[t]/(F[t] P[t]). This has run-on effects on the values of ipEUR2, ipEUR3 and eurOpt. Next the third equation in the article establishing consistency for both sides of the FX call option on EUR/USD is incorrect in that the Radon-Nikodym derivative

dUSD/ dEUR = Exp[(r-q) t]*F0/F[t]

hence the equation should be

E^(-r t) Subscript[E, USD] ( Max[ Subscript[F, t]-K,0]) = E^(-q t) Subscript[F, 0]   
Subscript[E, EUR] (  (1/Subscript[F, t])  Max[Subscript[F, t]-K,0] ) 

and this is also consistent with your definition of eurOpt. With all of these changes we get a difference between the EUR and USD versions of the FX option of -6 10^(-4), small but not zero, but this is consistent with Jensen's inequality.

I may have missed something in the subtlety of the arguments but the SDE definition of F[t] is explicitly defined at the outset. Thanks again for any help in explaining this discrepancy

Michael

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