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?
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
- Forward price=$0.894461
- $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