Final answer:
The arbitrage-free forward price of silver for a 9-month forward contract is calculated using the spot price, storage costs, and risk-free interest rate. The value of a short position in this contract after 6 months depends on the difference between the original forward price and the new forward price .
Step-by-step explanation:
The student's question involves calculating the arbitrage-free forward price and the value of a short position in a forward contract based on the spot price of silver. Given a spot price of $23 per ounce, storage costs of $0.24 per ounce per year payable quarterly, and a 5% annual risk-free interest rate, the computation requires the use of financial mathematics to determine the fair value of the forward contract for delivery in 9 months.
For part (a), the arbitrage-free forward price F is calculated using the formula F = S * exp((r + u - d) * T), where S is the current spot price, r is the risk-free interest rate, u is the storage cost, d is the convenience yield (which is zero in this case as it is not provided), and T is the time to delivery in years. The forward price would need to be adjusted to reflect the storage costs paid quarterly in advance.
For part (b), the value of the short forward position after 6 months, with the spot price at $20, would be determined by the difference between the original contract price and the new no-arbitrage forward price at the 6-months mark, with the same formula being adapted to account for the remaining 3 months until the contract's maturity.