Pricing FX digital call on EUR, EURUSD

Joined
5/9/13
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I'm trying to price an EURUSD call on EUR, binary option as,
\(\)
\(C_t = N^{EUR}D_T^{EUR}\mathbb{E}^{EUR}\left[1_{X_T > K}\right]\)

where \(X_T\) is EURUSD underlying.

I'm getting,

\(C_t = N^{EUR}D_T^{EUR}\Phi(d_1)\)

and it seems that this premium should be in EUR. However, Bloomberg returns a EUR price equal to,

\(C_t = X_0N^{EUR}D_T^{EUR}\Phi(d_1)\)

Bloomberg quotes this as the EUR price, but it seems this should be in USD. There is a field where I've chosen the notional \(N\) to be in EUR.

Any help is much appreciated.
 
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