Swap annuity
Definition · Level 11 · Pricing toolkit
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The value today of receiving 1 on each fixed-leg date: Σ τ·DF. It sets the fixed leg’s value (rate × annuity) and, with the notional, a swap’s change in value per basis point.
Example
Discount factors 0.97 and 0.94, yearly payments → annuity 1.91.
Where Tradecraft teaches it
Level 11 · Pricing toolkit, in the lesson “FRAs & interest rate swaps”: Lock a future rate with a forward rate agreement, swap fixed for floating, and find the fixed rate that makes a swap worth zero.
Related terms
- FRA (forward rate agreement)A contract that fixes today the interest rate for a future period; a 3×6 fixes the 3-month rate from month 3 to month 6.
- Par swap rateThe fixed rate that makes a new swap worth zero: (1 − DFn) ÷ Σ τ·DFi, the floating payments’ value divided by the annuity.
- Payer swapAn interest rate swap in which you pay the fixed rate and receive the floating rate.
- 0.4 ruleAt-the-money-forward call or put ≈ 0.4 × S × σ × √T (small dividends, modest σ√T), because 1/√(2π) ≈ 0.4.
- Arbitrage boundsPrice limits any option must respect, or someone locks in a riskless profit: call ≤ S, European put ≤ K·e^(−rT), call ≥ max(0, S − K·e^(−rT))…
- Backward induction (pricing tree)Solving a problem from the last step back to the first.