Question

Sliver sells at $1,203 per ounce and it has a storage cost U paid at the beginning of each 6-month period. The risk-free interest rate is 4% per annum continuously compounded. The 3-month futures price is $1,237.504. Assuming that Silver doesn’t have a convenience yield.

(a) what is the storage cost? (b) is there an arbitrage if the 1 year future price is 1274

for the part A is there really have a cost due to the six year period; which does not connect with the 3 month contract.

Answer 1

a) Future Contract Price of Silver =

(Current Price of Silver x continous rate for n period) + (Storage cost x continous rate for n period)

Therefore, 1237.504 = (1203 X ) + (Storage Cost X )

or 1237.504 = (1203 x 1.0202) + (Storage Cost x 1.0202)

or, 1237.504 = 1227.30 + (1.0202 x Storage Cost)

or, Storage Cost = 10 (approx)

b) Let us calculate the should be 1 year Future Contract price

= (Current Price of Silver x continous rate for 1 year) + (Storage cost x continous rate for 1 year)

=  (1203 X ) + (10 X ) = 1262.50

We can see that the Should be Future Contract price (1262.50) is less than the Actual Future Contract Price (1274). Therefore there exists an arbitrage opportunity. We can earn arbitrage profit by Selling the 1 year Future Contract at 1274.