Enter Values
Understanding Forward Pricing
- No-Arbitrage: Forward price prevents risk-free profit
- Contango: F > S (forward premium when r > 0)
- Backwardation: F < S (rare, typically with benefits)
- Convention: Uses discrete annual compounding
Forward Price Result
Formula Breakdown
Understanding the Result
Forward Premium
When F > S, the forward is at a premium (contango). This reflects the cost of financing the asset purchase. Holding an asset has opportunity cost equal to the risk-free rate.
No-Arbitrage Pricing
The forward price is determined by no-arbitrage. If F ≠ S₀(1+r)^T, arbitrageurs can earn risk-free profits through cash-and-carry or reverse cash-and-carry strategies.
Forward Premium/Discount Guide
| Premium % | Status | Interpretation |
|---|---|---|
| > 10% | High Premium | Strong contango (high rates or long maturity) |
| 5% to 10% | Moderate Premium | Normal forward premium |
| 0% to 5% | Low Premium | Minimal time value |
| -5% to 0% | Low Discount | Slight backwardation |
| < -5% | High Discount | Strong backwardation (negative rates) |
Understanding Forward Pricing
What is a Forward Price?
The forward price is the delivery price that makes a forward contract have zero initial value. It's determined by no-arbitrage pricing:
- Cost of Carry: The forward premium reflects the financing cost of holding the asset
- No Upfront Payment: Unlike buying the asset directly, entering a forward costs nothing initially
The No-Arbitrage Argument
Why does the forward price equal S₀(1+r)T? Consider these strategies:
- Cash-and-Carry: Borrow $S₀, buy the asset, enter short forward at F. At expiration: sell asset for F, repay S₀(1+r)T. Profit = F - S₀(1+r)T.
- Reverse Cash-and-Carry: Short sell the asset for S₀, invest at r, enter long forward at F. At expiration: receive S₀(1+r)T, buy asset at F, return to lender. Profit = S₀(1+r)T - F.
If F ≠ S₀(1+r)T, one of these strategies yields a risk-free profit, violating no-arbitrage.
Contango vs. Backwardation
Contango (F > S)
Normal condition when r > 0. Forward price exceeds spot due to financing costs.
Backwardation (F < S)
Occurs when holding benefits (dividends, convenience yield) exceed financing costs.
Relationship to Forward Value
-
At Initiation
Forward value = 0 (the forward price is chosen to make this true)
-
During Life
Value changes as spot moves: Vt = St - F₀(T)/(1+r)(T-t)
-
At Expiration
VT = ST - F₀(T) (no discounting needed)
Frequently Asked Questions
Disclaimer
This calculator is for educational purposes only and does not constitute financial advice. Actual forward prices may differ due to transaction costs, market frictions, and asset-specific factors. Always consult with a qualified financial advisor.
