Hi @Hamam As I've written (here in the forum) many times, I don't like the foreign/domestic distinction for this application; ie., IRP is just cost of carry. Think of how we price the forward of a consumption commodity like corn: we use F(0) = S(0)*exp[(r+u)*T] to get a forward price in USD where "r" is the U.S. risk-free rate. Similarly, I find it very easy to add the interest rate associated with the quote currency, and subtract the interest rate associated with the base currency because the base currency is the commodity. Almost no thinking required!
So, in question 166.1., if our spot exchange rate is 0.1250 that's JPYUSD 0.0125 which is utilizing the BASE/QUOTE sequence, or we could add the dollar sign to be redundant: JPYUSD $0.0125 refers to $0.0125 USD per one unit of JPY. Here JPY is the commodity and its interest rate is like a dividend. USD is the quote currency; USD is being used to buy JPY, much like it might by corn. Because USD is the quote currency, the forward price must add the US interest rate: F(0) = S(0)*exp[(r_USD - r_JPY)*2]. Similarly, because JPY is the commodity, its dividend (in the COC) must subtract, and its dividend is its interest rate. So, it must be F(0) = $0.0125*exp[(2% -0%)*2].
If we started with a spot exchange rate of JPY 80.00 or USDJPY ¥80.00, then JPY is the quote currency and USD is the commodity. In this case we need F(0) = S(0)*exp[(r_JPY - r_USD)*2] = ¥80.00*exp[(0% - 2%)*2] = ¥76.8632 because JPY is the "buying" currency and JPY is the commodity with a dividend that must be subtracted in the COC. Thanks,