Question

Consider a forward contract on gold. Each contract covers 100 ounces of gold and matures one year from now. Suppose it costs $2 per ounce per year to store gold with the payment being made at the end of the year. Assume that the spot price of gold is $1300 per ounce, the continuously compounded risk-free interest rate is 4% per annum for all maturities.

a) In the absence of arbitrage, find the current forward price. Show your calculations.

b) Assume you immediately sell one contract. What is the value of your position in 3 months’ time if the gold spot price has fallen to $1200 per ounce and interest rates have not changed? Show your calculations.

Answer 1

a) One year Forward price per ounce of Gold

= Spot price + interest cost+ Storage cost

=1300*exp(0.04*1) + 2

=$1355.05 per ounce which is the forward price in absence of arbitrage

b) Theoretical forward price per ounce after 3 months (9 months remaining)

= 1200*exp(0.04*9/12) + 2*9/12 (assuming proportional storage cost)

= $1238.05

Value of Short forward contract per ounce after 9 months

= $1355.05 - $1238.05

=$117.01

So, value of contract (with 100 ounce) today

=100 *117.01*exp(-0.04*9/12)

=$11355.04