Futures Price Calculator — Free Online Pricing Tool

How to Use the Futures Price Calculator

This calculator applies the cost-of-carry model to determine the theoretical fair value of a futures contract. Whether you are analyzing commodity futures, financial derivatives, or currency forwards, follow these steps for accurate pricing.

1. Enter the current spot price. This is today's market price for the underlying asset. For commodities like gold or oil, use the current spot market price. For stock index futures, use the current index level. For currency pairs, use the current exchange rate. The spot price is the foundation of the entire calculation.
2. Set the risk-free interest rate. Enter the annualized rate, typically benchmarked to government bond yields of the appropriate maturity. For a 3-month futures contract, use the 3-month Treasury bill rate. For a 1-year contract, use the 1-year Treasury yield. The default value uses the current approximate Treasury yield.
3. Enter the storage cost rate. For physical commodities, enter the annual cost of storing the asset as a percentage of its value. This includes warehousing, insurance, and any deterioration costs. For financial assets like stocks, bonds, or currencies, set this to 0% since there are no physical storage costs.
4. Set the time to expiry. Enter how long until the futures contract expires, in years. Use 0.25 for a 3-month contract, 0.5 for 6 months, 1.0 for one year. Longer expiry periods result in larger basis values because carrying costs accumulate over time.
5. Enter the convenience yield. For commodities, this represents the benefit of holding the physical asset. For dividend-paying stocks or stock indices, enter the annual dividend yield. For bonds, enter the coupon rate. Set to 0% if there is no income or convenience benefit from holding the asset.
6. Analyze the results. The calculator shows the theoretical futures price, the basis (positive for contango, negative for backwardation), the basis as a percentage of the spot price, carrying costs, and convenience yield values. Compare the theoretical price against the actual market futures price to identify potential mispricings.

Understanding the Cost-of-Carry Formula

The cost-of-carry model is the standard approach for theoretical futures pricing. It reflects the principle of no-arbitrage: the futures price should equal the cost of buying the asset today and carrying it until delivery.

The Core Formula

Where:

• F = Theoretical futures price
• S = Current spot price of the underlying asset
• r = Annualized risk-free interest rate (as a decimal)
• s = Annualized storage cost rate (as a decimal)
• y = Annualized convenience yield rate (as a decimal)
• T = Time to expiry in years
• e = Euler's number (approximately 2.71828)

Basis Calculation

Step-by-Step Calculation Example

Calculate the fair value of a 1-year gold futures contract with a spot price of $2,000, risk-free rate of 4%, storage cost of 0.5%, and zero convenience yield:

1. Identify variables: S = $2,000, r = 0.04, s = 0.005, y = 0, T = 1
2. Calculate the exponent: (0.04 + 0.005 - 0) × 1 = 0.045
3. Calculate e raised to the exponent: e^0.045 = 1.04603
4. Calculate futures price: $2,000 × 1.04603 = $2,092.06
5. Calculate basis: $2,092.06 - $2,000 = $92.06 (4.60% contango)

The theoretical futures price of $2,092.06 reflects the cost of financing ($80 at 4%) and storing ($10 at 0.5%) the gold for one year. If the actual market futures price differs significantly from this theoretical value, it may signal an arbitrage opportunity or the market pricing in factors not captured by the simple cost-of-carry model.

Practical Futures Pricing Examples

These examples demonstrate how the cost-of-carry model applies across different asset classes, from physical commodities to financial instruments.

Crude Oil Futures

An energy trader, Carlos, wants to determine the fair value of a 6-month crude oil futures contract. The current spot price is $75/barrel, the risk-free rate is 4%, storage costs are 2% annually (including insurance and tank rental), and the convenience yield is 3% (reflecting tight physical supply). F = $75 × e^((0.04 + 0.02 - 0.03) × 0.5) = $75 × e^(0.015) = $75 × 1.01511 = $76.13. The basis is $1.13 (1.5% contango). If the market futures price is $77.50, the futures are trading at a premium to theoretical fair value, potentially indicating market expectations of tighter supply ahead.

Stock Index Futures

Portfolio manager Tamara wants to price a 3-month S&P 500 futures contract. The index is at 5,200, the risk-free rate is 4.5%, storage cost is 0% (financial asset), and the dividend yield of the index is 1.4%. F = 5,200 × e^((0.045 + 0 - 0.014) × 0.25) = 5,200 × e^(0.00775) = 5,200 × 1.00778 = 5,240.47. The basis is 40.47 points (0.78% contango). This basis reflects the net cost of carry: financing at 4.5% minus dividend income of 1.4%. Tamara can compare this theoretical price against actual E-mini S&P 500 futures quotes to assess fair value.

Currency Futures

International trader Yuki analyzes EUR/USD 1-year futures. The spot rate is 1.0900, the US risk-free rate is 4.5%, and the Eurozone rate (convenience yield for the euro holder) is 3.5%. F = 1.0900 × e^((0.045 + 0 - 0.035) × 1) = 1.0900 × e^(0.01) = 1.0900 × 1.01005 = 1.1010. The basis of 0.0110 (1.01% contango) reflects the interest rate differential favoring the US dollar. This aligns with covered interest rate parity: the higher-yielding currency (USD) trades at a forward discount relative to the lower-yielding one (EUR).

Futures Pricing Tips and Complete Guide

Understanding futures pricing and the cost-of-carry model is essential for anyone involved in commodities trading, financial derivatives, or portfolio hedging. Here is a comprehensive guide to applying these concepts effectively.

Identify Arbitrage Opportunities

When the actual futures price significantly deviates from the theoretical cost-of-carry price, an arbitrage opportunity may exist. If futures are trading above fair value (overpriced), a trader can sell the futures and simultaneously buy the spot asset, financing the purchase at the risk-free rate. If futures are trading below fair value (underpriced), the reverse trade applies: buy futures and sell the spot asset short. In practice, transaction costs, margin requirements, and market frictions reduce the profitability of such trades, but the principle keeps futures prices anchored near their theoretical values.

Understand Roll Yield in Futures Portfolios

Investors who hold commodity futures through rolling (selling expiring contracts and buying the next month) are exposed to roll yield. In contango markets, rolling costs money because the next contract is more expensive. In backwardation, rolling generates positive returns. Over time, roll yield can significantly impact total returns. For example, crude oil futures in persistent contango can underperform the spot price by 5-10% annually due to negative roll yield, even if the spot price is rising.

Adjust the Model for Different Asset Types

The cost-of-carry model is versatile but requires appropriate parameter selection for each asset class. For precious metals, storage costs are low (0.2-0.5%) and convenience yield is typically zero. For agricultural commodities, both storage costs and convenience yields can be substantial and seasonally variable. For financial assets, storage cost is zero but income yield (dividends or coupons) plays a critical role. Always use asset-class-appropriate parameters for accurate pricing.

Common Mistakes to Avoid

• Ignoring the convenience yield for physical commodities. Leaving convenience yield at zero for commodities with tight physical supply will overestimate the futures price. Research the current supply-demand dynamics for the specific commodity before setting this parameter.
• Using the wrong risk-free rate maturity. Match the risk-free rate to the futures contract's time to expiry. Using a 10-year Treasury rate for a 3-month futures contract misrepresents the actual financing cost.
• Confusing annualized rates with periodic rates. The calculator expects annualized rates. If you have a 3-month storage cost of 0.5%, the annualized rate is approximately 2%, not 0.5%. Always annualize before entering values.
• Assuming the model captures all market dynamics. The cost-of-carry model provides a theoretical fair value but does not account for supply-demand imbalances, speculative positioning, regulatory changes, or market sentiment. Use it as a baseline, not a definitive price prediction.
• Neglecting transaction costs in arbitrage analysis. Theoretical arbitrage opportunities often disappear once you factor in bid-ask spreads, commissions, margin costs, and the operational complexity of executing simultaneous spot and futures trades.