Suppose the current price of an ounce of gold is $1400 and the forward price for

Question

Suppose the current price of an ounce of gold is $1400 and the forward price for delivery of an ounce of gold in six months is $1435 and the forward price for delivery of one ounce in one year is $1470. The current six-month interest rate (annualized) is 4.0% and the current one-year rate is 4.5%. What is the fixed price of a one-year gold swap that has payments in six months and one year (to two digits accuracy)? A gold swap pays the difference between the fixed price and the actual price of gold at the two dates times a nominal size.

Explanation / Answer

Current price =1400

Forward Price (6 month) =1435

Forward Price (1 year) =1470

6 month rate =4%

1 year rate =4.5%

Let the fixed price be x

P.V of fixed payment =1400*x*(1/(1+0.04/2)+1/(1+0.045))=x*1.93733*1400

P.V of floating =1435/ (1+0.04/2) +1470/(1+0.045)= 2813.561

At swap initiation

P.V of fixed payment= P.V of floating

x* 1.93733*1400 =2813.561

x=2813.561/ (1.93733*1400)=1.037349

Fixed payment =1.037349-1 =3.7349%

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