Pricing and Valuation of Futures Contracts

How futures are priced at inception exactly like forwards, how daily settlement through a margin account changes their value over time, how short-term interest rate futures are quoted and compared with FRAs, and why forward and futures prices can differ: interest rate correlation and volatility, the convexity bias, and the narrowing effect of central clearing.

1. 1. Pricing a futures contract at inceptionAt inception a futures contract is worth zero and its price is set by the same carry arithmetic as a forward: the spot price, adjusted for income and costs, grown at the risk-free rate to maturity.Video · 5 minFree11 min
2. 2. Mark-to-market: futures versus forwardsA forward's gain or loss builds up unsettled until maturity, while a futures contract settles it in cash every day and resets its value to zero; by maturity the cumulative realized results are about the same.14 min
3. 3. Short-term interest rate futures versus FRAsShort-term interest rate futures are quoted as 100 minus the rate, so a long gains when the market reference rate falls, and every basis point is worth a fixed amount: notional × 0.01% × period.Video · 5 min12 min
4. 4. Why forward and futures prices can differDaily settlement makes futures gains and losses arrive earlier, so when futures prices move with interest rates, one contract becomes more valuable to hold and its price is bid above the other.11 min
5. 5. Convexity bias and the effect of central clearingInterest rate futures pay a fixed amount per basis point, while an FRA's settlement is discounted at the new rate and so is non-linear; meanwhile central clearing has given OTC forwards futures-like margining, shrinking the gap between the two.13 min