Rates Derivatives

Swaption

Also known as: Swap option, Payer / receiver swaption

An option to enter a swap — the instrument through which the market prices interest-rate uncertainty itself.

Asset class
Rates derivatives
Instrument type
Option on a swap
Traded
OTC
Typical users
Mortgage hedgers, insurers, vol traders
A payer swaption at expiry: valuable when the swap rate has risen above the strike.
KPayer swaptionUnderlying price at expiryProfit / loss
BeginnerWhat is it, really?

A swaption is an option whose underlying is an interest rate swap. A payer swaption gives the right to enter a swap paying a fixed rate agreed today; it pays off if rates rise. A receiver swaption is the right to receive that fixed rate; it pays off if rates fall.

Names follow a "period into period" convention: a "1y into 10y" swaption expires in one year, on a swap that then runs ten more.

Who needs this? Anyone whose future depends on future rates: a company planning to borrow in a year buys a payer swaption as a rate ceiling that still lets it enjoy lower rates; insurers and pension funds buy receivers to protect against rate collapses that balloon their liabilities.

Key intuition: the swap market says where rates are expected to go; the swaption market prices how wrong that expectation might be. It is the market for interest-rate uncertainty.
IntermediateHow it works in practice

Settlement and structure

  • Physical: exercise into the actual swap; cash-settled: receive the swap's value at expiry (conventions differ by currency).
  • Premium: paid upfront, quoted either in cash or — the trader's native unit — in implied volatility.
  • The grid: quotes span expiry × swap tenor (1m into 2y … 10y into 30y), forming the volatility surface ("vol cube" with strike as the third axis).

Who drives the flows

  • MBS hedgers: US mortgage books are short vol (homeowners' prepayment options); hedging them makes desks structural swaption buyers.
  • Insurers/LDI: long-dated receivers hedge guarantees written to policyholders.
  • Callable debt: every callable bond issued embeds a swaption; issuers/dealers recycle that vol into the market.
  • Exotic desks: swaptions are calibration targets for anything Bermudan or path-dependent.

Straddles: trading pure uncertainty

Buying payer + receiver at the same strike (a straddle) profits from large moves either way — the standard vehicle for "rates will get wild" views around elections, inflation prints and policy pivots.

Worked example: a 1y-into-10y payer struck at 3.5% costs 90bp of notional. A year later the 10-year swap rate is 4.3% → the underlying swap is worth ≈ 6.4% of notional (80bp × duration 8) — a 7x payout. At 3.4%, the swaption expires worthless.
AdvancedPricing & valuation

Pricing in the annuity measure

The swap rate \(S_t\) is a martingale under the measure whose numéraire is the annuity \(A_t = \sum \delta_i P(t, T_i)\). A payer swaption struck at \(K\) is then a call on \(S_T\):

$$ V_{payer} = A_0 \,\mathbb{E}^{A}\big[(S_T - K)^+\big] $$

With normal (Bachelier) dynamics \(dS = \sigma_N\, dW\) — the market standard since rates went to zero and below:

$$ V_{payer} = A_0\Big[(S_0 - K)\,N(d) + \sigma_N \sqrt{T}\, \varphi(d)\Big], \qquad d = \frac{S_0 - K}{\sigma_N\sqrt{T}} $$

Quotes are in normal vol (bp/year); lognormal (Black) quoting survives in some corners.

The smile and its models

Across strikes, implied vol forms a smile; the workhorse parameterisation is SABR (\(\beta\) controlling backbone, \(\rho\) skew, \(\nu\) smile curvature), fitted per expiry-tenor point. For products depending on the joint dynamics of many rates (Bermudans, callables), desks calibrate term-structure models — LMM (Libor/forward market models) or cheaper Hull–White/LGM — to the swaption grid.

Greeks with a twist

Vega splits by expiry-tenor bucket; delta is an annuity-weighted swap DV01; and cash-settled vs. physical conventions create measurable convexity differences (the famous CMS-linked corrections). Vol itself has term structure and its own risk premium — systematically selling rate vol has been a documented (and occasionally catastrophic) carry trade.

Practitioner note: the swaption surface is the rates market's central nervous system — MBS, callables, structured notes, LDI and exotics all shake the same grid. Watch 1y10y normal vol as the market's headline "rate fear" gauge.