Explain the pricing of interest rate forwards and futures, and work out their no-arbitrage value and say what it means
The idea
An FRA fixes today the rate for a future borrowing period, implied by two spot market reference rates. For an FRA covering the period from h to h + m, [1 + MRR(h + m) × t(h + m)] ÷ [1 + MRR(h) × t(h)] − 1 gives the period rate, annualised by dividing by the accrual fraction m. Later, the long (pay fixed) gains when rates rise: value = (new FRA rate − original FRA rate) × accrual fraction × notional ÷ (1 + spot rate to the loan's end × its accrual fraction). Rate futures are quoted as 100 minus the rate, so rising rates help the short. The trap is discounting only to the FRA's start date or forgetting the accrual fraction.
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