In pricing of forward on currencies, why do we do spot exchange rate discounted at the foreign interest rate - forward rate discounted at the domestic interest rate.
I am confused as to which interest rates are used where?
Can someone explain this to me.
Because of the arbitrage relationship:
S(f/d) (1+rf) = F(f/d) (1+rd)
S(f/d) (1+rf) / F(f/d) = (1+rd)
This is saying that if you start with one unit of the domestic, convert it to foreign, earn the foreign return, and forward convert it back tot he domestic currency, it should equal the domestic return.
I understand that part but I am still not clear as to why we foreign interest rate to discount the spot exchange rate and domestic interest rate to discount the forward rate?
Because the math doesn’t lie…
S(f/d) (1+rf) = F(f/d) (1+rd) --> S(f/d) / (1+rd) = F(f/d) / (1+rf)
I think my notation is backwards to yours but the point remains the same…
You are receiving the foreign currency
You are delivering the domestic currency
You discount what you receive, the foreign currency by the foreign rate
You discount what you are delivering (the domestic) by the domestic rate.
That’s what you do, not why you do it.
I wrote an article that may help here: http://financialexamhelp123.com/valuing-a-currency-forward-whence-came-that-formula/