Why do we discount @ price currency vs. the base currency when valuing a forward contract prior to expiration?
Are you talking about the formula in which we appear to discount the spot price at the base currency’s risk-free rate and appear to discount the (original) forward rate at the price currency’s risk-free rate?
No, this formula below:
((FPt - FP) * # of contracts)/(1+interest rate price currency(days/360)
I am confused why we use the price currency interest rate vs. the base currency interest rate.
My guess, The numerator is in the same currency you discount.
The numerator is in terms of the base currency, so why not discount back at the base currency?
Yes: the exchange rates in the numerator are PC/BC, and the number of contracts is the amount of base currency to be delivered, so the units in the numerator are:
PC/BC × BC = PC
This is the mark-to-market formula from Econ, and is equivalent to the (very different looking) formula from derivatives.