What is the delta of a short position in 2,000 European call options on silver futures? The
options mature in 11 months, and the futures contract underlying the option matures in
12 months. The current nine-month futures price is $16 per ounce, the exercise price of the
options is $16, the risk-free interest rate is 8% per annum, and the volatility of silver futures
prices is 15% per annum.
i.	What initial position in nine-month silver futures is necessary for delta hedging?
ii.	If silver itself is used, what is the initial position?
iii.	If one-year silver futures are used, what is the initial position?
Assume no storage costs for silver.