  Option written on several foreign exchange rates (FXRs) depends on
correlation between the rates. To evaluate the option, historical estimates for
correlations can be used but usually they are not stable. More significantly,
pricing of the option using these estimates is usually inconsistent to the
traded vanilla contracts. To price options written on several FXRs with the
same denominating currency, financial practitioners and traders often use
implied correlations calculated from implied volatilities of FXRs that form
"currency triangles". However, some options may have underlying FXRs with
different denominating currencies. In this paper, we present the formula for
the implied correlations between such FXRs. These can be used for valuation,
for example, barrier option on two FXRs with different denominating currencies
where one FXR determines how much the option is in or out of the money at
maturity while another FXR is related to the barrier. Other relevant options
are straightforward.
