Pricing and valuing FX forwards

In short

• Quotes are price currency per unit of base currency: $S_{f/d}$. Here f is the price (foreign) currency and d the base (domestic) currency.
• Forward price: $F_{0,f/d}(T) = S_{0,f/d}\,e^{(r_f - r_d)T}$.
• The currency with the lower interest rate trades at a forward premium; the one with the higher rate at a forward discount.
• MTM value of a long (buy base currency) forward: $V_t(T) = S_{t,f/d} - F_{0,f/d}(T)\,e^{-(r_f - r_d)(T-t)}$, per unit of base currency.
• A wider differential $r_f - r_d$ makes the price currency depreciate on a forward basis and raises the value of a long-base position.