The current price of silver is 9 per ounce. The storage...

The current price of silver is $\$ 9$ per ounce. The storage costs are $\$ 0.24$ per ounce per year payable quarterly in advance. Assuming that interest rates are $10 \%$ per annum for all maturities, calculate the futures price of silver for delivery in nine months.

Key Concepts

Futures Pricing

Futures pricing is the process of determining the theoretical price at which a commodity should be exchanged in the future, using the current spot price and adjustments for storage and financing costs. This calculation ensures that no arbitrage opportunities exist between the spot and futures markets, maintaining market equilibrium.

Interest Rate Adjustments

Interest rates play a pivotal role in the cost-of-carry model because they represent the financing cost related to holding an asset. When the interest rate is given on an annual basis, it needs to be appropriately converted to the period relevant to the problem (such as quarterly or for a nine-month term). This adjustment is crucial for accurately accumulating or discounting costs over non-annual time frames.

Cost of Carry

The cost-of-carry model explains how the futures price is determined from the spot price through adjustment for all costs and benefits associated with holding the asset until delivery. These costs commonly include financing costs (interest rates), storage expenses, insurance, and any benefits such as dividends or convenience yields. In arbitrage-free pricing, the futures price must cover these factors to prevent riskless profit opportunities.

Storage Costs

Storage costs represent the expense incurred for holding a physical commodity over time. When these costs are incurred periodically or in advance, they must be properly adjusted or compounded over the delivery period. How and when these costs are paid (e.g., quarterly in advance) can affect the effective cost of carry and therefore the calculation of the futures price.

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