Question

The spot price of silver is $20 per ounce. The storage costs are $0.30 per ounce per year payable quarterly in advance. Assuming that interest rates are 4% per annum for all maturities, calculate the futures price of silver for delivery in 12 months.

Answer 1

storage cost per year = 0.3

per quarter storage costs are 0.3/12 = 0.075

pv of storage costs is =

0.075 + 0.075/e^(0.04*3/12) + 0.075/e^(0.04*6/12) + 0.075*e^(0.04*9/12) = 0.2955

futures price = (spot + pv of storage costs)*e^(rate)

= (20+0.2955)*e^0.04 = 21.1237

so futures price for delivery in 12 months is 21.1237