Question

Considering the following, the US continuously compounded risk free rate is 5% and Swiss risk free rate is 3%, and the currency spot exchange rate is $0.89 USD per CHF (Swiss Franc).

A.    Using the Currency continuous pricing model, what is the appropriate “Interest Rate Parity” forward price on a contract expiring in 3 months?

B.     For a 3-month forward contract, if a dealer quotes a forward price on USD per CHF as $0.90 per CHF, then answer the following two questions:

a.      Is the dealers’ quote under or overpriced?

To take advantage of the situation, what should an arbitrageur do to make a profit?

Answer 1

Forward Rate=Spot Rate*((1+domestic interest rate)/(1+foreign interest rate))

Spot rate=$0.89of domestic currency per unit of foreign currency (CHF-Swiss Franc)

Domestic interest rate=5% continuously compounded=0.05 continuously compounded

Foreign interest rate= 3% continuously compounded=0.03 continuously compounded

Period in years=3/12=0.25

Amount of $0.89 after three months at 5% continuously compounded=0.89*(e^(0.05*0.25) )

Amount of domestic currency=0.89*1.012578=$0.901195

Amount of foreign currency(CHF) after 3 months=1*(e^(0.03*0.25) )=1.007528

Forward Rate=(0.901195/1.007528)=$0.894461 per CHF

1. Forward price=$0.894461
2. $0.90 is overpriced since the rate should be $0.894461 as per interest rate parity

To take advantage of the situation, arbitrageur should sell at $90 per CHF to make a profit