The exchange rate of one Swiss franc is $1.37. The price of a 6-month U.S. zero coupon bond is $0.92, and the price of a 1-year U.S. zero coupon bond is $0.89. Forward contracts are available on the Swiss franc. The forward price is $1.35 for a 6-month forward and $1.39 for a 1-year forward.
What should be the fixed rate for a 1-year semiannual interest rate swap in Switzerland? Write your answer in unit of percentage points.
To calculate the fixed rate for a 1-year semiannual interest rate swap in Switzerland, we need to use the concept of present value.
First, let's calculate the present value of the cash flows for both parties of the swap. The fixed rate is the rate at which the present value of the fixed leg cash flows equals the present value of the floating leg cash flows.
Let's assume the fixed leg pays a semiannual coupon based on the fixed rate, and the notional principal is 1 Swiss franc. The floating leg pays a semiannual coupon based on the 6-month LIBOR rate in Switzerland.
To calculate the present value of the fixed leg, we need to discount the semiannual coupon payments using the current market rates. The current market rate for a 6-month zero coupon bond is $0.92, and for a 1-year zero coupon bond is $0.89. Therefore, the present value of the fixed leg for each period can be calculated as follows:
PV_fixed = (Coupon_payment / (1 + market_rate/2)^period_number)
For a 1-year swap, we have two periods (semiannual), so the present value of the fixed leg is:
PV_fixed = (Coupon_payment / (1 + 0.89/2)^1) + (Coupon_payment / (1 + 0.89/2)^2)
To find the coupon payment, we need to solve for it. The present value of the fixed leg should equal the present value of the floating leg, which is the notional principal times the 6-months LIBOR rate.
For a 1-year semiannual swap, the present value of the floating leg is:
PV_floating = (Notional_principal * 6_months_LIBOR_rate) + (Notional_principal * 6_months_LIBOR_rate) / (1 + 6_months_LIBOR_rate/2)
To find the 6-month LIBOR rate, we can calculate it using the forward rate. The forward rate implies the future spot rate based on interest rate differentials between the two countries. Therefore, we can set up an equation using the forward rate and current spot rate as follows:
Forward_rate = Spot_rate * (1 + 6_months_LIBOR_rate/2)^2
Solving the equation for the 6-month LIBOR rate gives us:
6_months_LIBOR_rate = [(Forward_rate / Spot_rate)^(1/2) - 1] * 2
After calculating the 6-month LIBOR rate, we can substitute it into the equation for the present value of the floating leg.
Now we can solve for the coupon payment in the fixed leg equation by substituting the calculated values for the present value of the fixed leg and present value of the floating leg.
Once you have the coupon payment, you can convert it into a percentage and subtract the 6-month LIBOR rate to get the fixed rate for the 1-year semiannual interest rate swap in Switzerland.