Module 9 · Advanced
Swaptions & the Greeks
A swaption is an option to enter a swap at a set rate on a future date. A payer swaption lets you pay fixed — it pays off if rates rise (like a call on rates). A receiver lets you receive fixed — it pays off if rates fall(a put on rates). They're how you buy insurance on interest rates, or bet on them, with limited downside.
Because it's an option, its value depends on volatility, and it's priced with Black's formula on the forward swap rate. The Greeks measure the risks: delta (exposure to rates), vega (exposure to volatility — options are long vol), gamma (how fast delta changes), and theta (time decay — options bleed value each day). Turn up the vol and watch both the premium and vega jump.
🎛 Swaption pricer
2y into 5y payer swaption · forward 5.03%
$3,825,814
option premium
Delta
$272,988,016
per 1.00 in rate
Vega
$99,807
per 1% vol
Gamma
7.9e+9
Δ of delta
Theta
-$1,709
per day
A swaption is an option to enter a swap. A payer pays fixed (wins if rates rise); a receiver receives fixed (wins if rates fall). It's priced with Black's formula on the forward swap rate. The Greeks tell you the risks: delta (rate exposure), vega(volatility exposure — options love vol), gamma (how fast delta moves), theta (daily time decay). Crank the volatility up and watch the premium and vega climb. Educational tool — not investment advice.
Things to try
- • Crank volatility from 15% to 50% — the premium and vega soar. Options are a bet on vol.
- • Move the strike away from the forward — the option goes out-of-the-money and cheapens.
- • Switch payer ↔ receiver — delta flips sign (betting on rates up vs down).