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