Futures Forward Pricing
Category: Options & DerivativesCalculate theoretical futures prices, implied rates, and basis spreads based on cost-of-carry model
Pricing Model
Calculate the theoretical futures/forward price based on the cost-of-carry model for different asset classes.
Calculate the implied financing rate based on the observed futures price and the current spot price.
Analyze the basis (difference between futures and spot prices) across different expiration dates to identify term structure and potential trading opportunities.
Futures Contracts
| Contract | Expiry Date | Days to Expiry | Futures Price | Theoretical Price | Basis | Annual % Basis | Fair Value | Actions |
|---|---|---|---|---|---|---|---|---|
| 30 |
$
|
$100.75 | +$0.75 | +3.00% | Fair | |||
| 60 |
$
|
$101.25 | +$1.25 | +2.50% | Fair |
Term Structure & Basis Analysis
Analysis Summary
The term structure is in contango (upward sloping), which is typical in a normal market where carrying costs exceed income yield. The rate of increase is consistent with the cost-of-carry model.
No significant arbitrage opportunities detected based on the current inputs. All contracts are priced close to their theoretical values.
Market Data Reference
The following market rates are provided for reference only. For actual trading, please use the most up-to-date market data from authoritative sources.
| USD SOFR | 5.31% |
| USD 3M Treasury | 5.42% |
| USD 3M LIBOR | 5.50% |
| EUR €STR | 3.90% |
| GBP SONIA | 5.19% |
| S&P 500 | 1.43% |
| Dow Jones | 2.03% |
| NASDAQ 100 | 0.78% |
| FTSE 100 | 3.85% |
| DAX | 3.27% |
| Gold | 0.25-0.50% |
| Silver | 0.50-1.00% |
| Crude Oil | 1.00-3.00% |
| Natural Gas | 2.00-5.00% |
| Agricultural | 3.00-7.00% |
Understanding Futures & Forward Pricing
Futures and forward contracts are priced based on the cost-of-carry model, which accounts for the cost of holding the underlying asset until the contract's expiration date. The relationship between spot and futures prices is determined by interest rates, dividends/yields, storage costs, and convenience yields.
Cost-of-Carry Model Explained
The cost-of-carry model calculates the theoretical futures price based on the current spot price adjusted for all costs and benefits of holding the underlying asset until expiration:
The Basis
"Basis" refers to the difference between the futures price and the spot price (Basis = Futures - Spot).
- Positive basis (contango): Futures price > Spot price. This is the typical state when carrying costs exceed yields.
- Negative basis (backwardation): Spot price > Futures price. This occurs when convenience yields or other benefits of holding the physical asset exceed carrying costs.
- Basis convergence: As the contract approaches expiration, the basis converges to zero (or delivery costs in physical delivery contracts).
Arbitrage and Fair Value
The cost-of-carry model provides a theoretical "fair value" for futures prices. If market prices deviate significantly:
- Futures overpriced: Sell futures, buy spot (cash and carry arbitrage)
- Futures underpriced: Buy futures, short sell spot (reverse cash and carry)
- Arbitrage limitations: Transaction costs, margin requirements, borrowing constraints, and short-selling restrictions may limit perfect arbitrage
Asset-Specific Considerations
Equity Index Futures
For equity indices, dividend yields reduce the cost of carry. Index futures pricing must account for all expected dividends during the contract period. In practice, the dividend estimate is often an annualized yield based on projected payments.
Currency Futures
Currency futures reflect interest rate differentials between two currencies. Higher domestic interest rates typically result in futures trading at a premium to spot (contango), while higher foreign rates lead to futures trading at a discount (backwardation).
Commodity Futures
Commodities often involve physical storage costs and may provide a convenience yield (benefit of holding the physical asset). Seasonal supply/demand patterns can create predictable shifts between contango and backwardation throughout the year.
Interest Rate Futures
These futures typically reflect market expectations of future interest rates. The pricing often relates to forward rate agreements and the shape of the yield curve, rather than simple cost-of-carry calculations.
Basis Spreads and What They Tell Us About Futures Pricing
Now that you've seen the results from the cost-of-carry futures calculator, you're looking at a rich snapshot of where the market thinks an asset should be priced in the future. Whether you're trading equity indices, currencies, or commodities, the output gives you a theoretical futures price, implied cost of carry, and basis. These are more than just numbers—they're signals that can influence how you time entries, structure trades, or spot mispricings in the futures curve.
Signals to Watch in Your Basis Output
The "basis"—the difference between the futures price and the spot price—is at the heart of this model. When used with awareness, it can help traders understand market sentiment and whether the current term structure supports long or short positions.
- Positive basis (Contango): The futures price is higher than spot. This is common when the cost of carry (like interest, storage, or insurance) outweighs any income from holding the asset.
- Negative basis (Backwardation): The spot price exceeds the futures price. This may occur when there's a high convenience yield or scarcity in the underlying asset.
- Flat basis: Futures are close to spot, typically occurring as contracts approach expiry or when markets are in equilibrium.
Your calculation shows a theoretical futures price of $101.76 with a spot price of $100, resulting in a basis of +$1.76 or +3.00% annualized. That’s a classic contango setup—what this implies is that carrying the position to maturity incurs a net cost, which is built into the futures premium.
What the Implied Rate Reveals
In the "Implied Rate" tab, you likely noticed a calculated rate of 5.60%. This is higher than the benchmark 3-month SOFR of 5.31% and Treasury rate of 5.42%, suggesting a slight premium in the futures market. When the implied financing rate differs significantly from market benchmarks, it can reflect:
- Expectations of future interest rate shifts
- Liquidity premia or demand/supply imbalances in the futures market
- Inaccuracies or delays in price discovery
Whether you’re considering arbitrage or managing a hedge, the implied rate helps assess whether the market is over- or under-pricing the cost of capital. Just note: “implied” doesn't mean “guaranteed”—it’s a derived figure, not an actual traded rate.
Common Takeaways from Your Basis Analysis
The basis analysis tool compares observed futures prices to theoretical fair values over different expiry dates. The results often point to one of these market conditions:
- Contango: A rising futures curve, often seen in commodities with ample supply and high storage costs
- Backwardation: A falling curve, which can indicate strong near-term demand or tight supply
- Flat curve: Market expects little change in underlying value, or short-term uncertainty is high
In your term structure chart, if you saw a steadily upward-sloping line, you're likely in a contango market. That matches the textbook cost-of-carry logic. But look for deviations—if a single contract is priced meaningfully above or below its theoretical value, that could point to an inefficiency or an opportunity (if transaction costs allow).
Risks and Trading Considerations
It’s tempting to jump on a mispriced contract, but keep a few practical risks in mind:
- Transaction costs: Arbitrage isn't free—fees, bid/ask spreads, and financing terms can eat into gains.
- Execution lag: Price discrepancies may resolve quickly. Fast execution is essential if you're aiming to trade on gaps.
- Shorting restrictions: Particularly with spot positions in equities or physical commodities, regulatory or margin rules might limit trade setups.
- Model assumptions: The tool uses constant rates and assumes no taxes or frictions. Reality is messier.
If the calculator flags a futures contract as underpriced, you’d typically consider buying the future and shorting the spot (reverse cash-and-carry). For overpriced contracts, the reverse might apply. But always check the fair value status and deviation threshold before acting. A 1% gap may be meaningful in some markets but noise in others.
Next Steps with Your Futures Price and Basis Model
Use the output from this calculator as a first step—not a final call. Here are some ways to follow through:
- Compare implied rates across different maturities to assess the yield curve slope
- Monitor basis trends over time for signs of shifting supply/demand dynamics
- Check your market’s actual dividend yields, storage costs, or interest differentials against the model’s assumptions
- Back-test how previous basis spreads aligned with market outcomes for your asset
Futures pricing models work best when paired with real-time market awareness. Stay curious, stay critical, and let the math inform—not override—your trading instincts.