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.
Options & Derivatives Tools:
What this calculates
The fair forward or futures price implied by spot and carry.
- Formula
F = S × e^((r − q)T), where q is the yield or convenience yield forgone- Worked example
- Spot 100, 5% rate, 2% dividend yield, one year: F = 100 × e^(0.03) ≈ 103.05.
- When to use it
- To check whether a quoted forward is rich or cheap against carry.
- Common mistake
- For FX the two interest rates drive it, not one. Using only the domestic rate gives the wrong forward and mis-prices the swap.