Learning Module 6
Pricing and Valuation of Futures Contracts
Key Outcomes Summary & Practice Problems
What you must be able to do
Curriculum Year: 2026
Compare the value and price of forward and futures contracts.
Explain why forward and futures prices differ.
1 · Futures Pricing at Inception
At inception, futures price f0(T) follows the same no-arbitrage logic as a forward — same cost-of-carry formula, same zero initial value.
The futures price for an asset with costs/benefits incorporates PV0(I) and PV0(C) exactly as for forwards.
f0(T) = S0(1 + r)T (discrete) | f0(T) = S0erT (continuous)
f0(T) = [S0 − PV0(I) + PV0(C)](1 + r)T
2 · MTM Valuation: Forwards vs. Futures Over Time
Feature | Forward | Futures |
|---|---|---|
Price after inception | Fixed at F0(T) for the life of the contract | Changes daily — resets to current settlement price ft(T) |
MTM value | Accumulates: Vt(T) = St − PV of F0(T); not settled until maturity | Resets to zero each day after settlement via margin account |
Cash exchanged | None until maturity | Daily variation margin |
Counterparty credit risk | Higher — unsettled MTM accumulates over the contract's life | Lower — daily settlement limits exposure to one day's change |
Cumulative gain/loss at maturity | Approximately the same for both contract types | |
The forward and futures contract's cumulative P&L converge by maturity — the difference lies in when and how that P&L is realized (lump sum vs. daily installments).
3 · Interest Rate Futures Mechanics
Short-term interest rate futures quote on a price basis, not a rate basis directly — an inverse price/yield relationship.
Long futures (lender) gains as prices rise (MRR falls); short futures (borrower) gains as prices fall (MRR rises).
A futures price above 100 implies a negative implied MRR for that period.
fA,B−A = 100 − (100 × MRRA,B−A)
Futures Contract BPV = Notional × 0.01% × Period
Contract | Gains from Rising MRR | Gains from Falling MRR |
|---|---|---|
Interest rate futures | Short futures | Long futures |
FRA | Long FRA (fixed-rate payer) | Short FRA (fixed-rate receiver) |
4 · Why Forward and Futures Prices Differ
Forward and futures prices are identical when (a) interest rates are constant, or (b) futures prices and interest rates are uncorrelated.
Positive correlation (futures price ↑ with rates ↑): long futures more attractive than long forward — gains can be reinvested at higher rates, losses occur when rates are low. Futures priced relatively higher.
Negative correlation: long forward more attractive than long futures (opposite logic) — forward priced relatively higher.
The more desirable contract type, given the correlation sign, tends to command the higher price.
5 · Convexity Bias (Interest Rate Futures vs. FRAs)
Interest rate futures have a linear price/yield relationship (fixed BPV regardless of rate direction).
FRAs have a non-linear settlement (their final payment is discounted at the prevailing MRR) — the percentage price change is larger in absolute value when MRR falls than when it rises.
This discounting-driven non-linearity is the convexity bias; it grows with longer discounting periods / greater rate volatility.
6 · Effect of Central Clearing on Forward vs. Futures Pricing
Central clearing has introduced futures-like margining for OTC derivative dealers, who often pass similar collateral requirements on to end users.
This reduces the cash-flow difference between ETD futures and OTC forwards — narrowing (though not eliminating) the pricing gap caused by daily settlement vs. lump-sum settlement.
In periods of market stress, futures positions may be forced to close out if a margin call can't be met; OTC forwards with more flexible (or no) collateral terms may remain outstanding longer.