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consider a something-or-nothing kind of option on uderlying EUR/USD. am i right in saying thatif notional is specified in USD then its a cash-or-nothing option and its BSM price in dollars is notional*e(-r_USD*time)*N(d2)and if notional is specified in EUR then its a asset-or-nothing option and its BSM price in dollars is notional*e(-r_EUR*time)*N(d1)*current exchange rate please correct me and tell me where am i wrong.

Want to know too.

my reasoning was price in the first case in dollars is exp(-r.t)*E(s_T>k) and price in latter case in dollars is exp(-r.t)*E(s_T | s_T>k)