Cost of Carry Model

The Cost of Carry Model determines the futures or forward price of an asset by considering the costs associated with holding (or "carrying") the asset until the contract's maturity. These costs include storage, insurance, and financing expenses, offset by any income the asset generates, such as dividends.

Formula:

[ F = S \times e^{(r + s - c)T} ]

Where:

• F: Futures price
• S: Spot price
• r: Risk-free interest rate
• s: Storage costs (as a percentage of the spot price)
• c: Convenience yield (benefit of holding the physical asset)
• T: Time to maturity (in years)

Example:

Assume:

• Spot price of oil (S): $100 per barrel
• Risk-free interest rate (r): 5% per annum
• Storage cost (s): 2% per annum
• Convenience yield (c): 1% per annum
• Time to maturity (T): 6 months (0.5 years)

Calculating the futures price (F):

[ F = 100 \times e^{(0.05 + 0.02 - 0.01) \times 0.5} ]

[ F = 100 \times e^{0.03 \times 0.5} ]

[ F = 100 \times e^{0.015} ]

[ F \approx 100 \times 1.0151 \approx 101.51 ]

Thus, the futures price is approximately $101.51 per barrel.