Calculator Inputs
Example Data Table
These examples use the same model as the calculator.
| Type | F | K | σ | T | A | DF | PV (approx) |
|---|---|---|---|---|---|---|---|
| Payer | 2.25% | 2.50% | 20.00% | 1.00 | 4.50 | 1.00 | 0.00403776 |
| Receiver | 2.25% | 2.00% | 18.00% | 0.50 | 4.10 | 0.99 | 0.00104905 |
| Payer | 3.10% | 3.00% | 22.00% | 2.00 | 3.80 | 0.97 | 0.01581757 |
Formula Used
This tool prices a European swaption using the Black (1976) model on the forward swap rate. It assumes lognormal dynamics for the forward swap rate and uses a fixed volatility input.
- F: forward swap rate
- K: strike rate
- σ: annualized volatility
- T: time to expiry (years)
- A: swap annuity (PV weights)
- DF: discount factor to settlement (optional)
d2 = d1 − σ √T
Payer PV = DF · A · [ F·N(d1) − K·N(d2) ]
Receiver PV = DF · A · [ K·N(−d2) − F·N(−d1) ]
The calculator also reports delta, vega, and a simple gamma estimate with respect to the forward rate. Use market conventions for annuity and discounting to match desk systems.
How to Use This Calculator
- Select payer or receiver swaption type.
- Choose units for rates and volatility, then enter inputs.
- Enter annuity (PV weights) for the swap tenor.
- Enable discount factor only if annuity is undiscounted.
- Press Calculate Swaption Price to view results.
- Use scenario shifts to see quick sensitivity changes.
- Download CSV or PDF to store the computed output.
FAQs
1) What is a payer swaption?
A payer swaption gives the right to pay fixed and receive floating. It gains value when the forward swap rate rises above the strike.
2) What is a receiver swaption?
A receiver swaption gives the right to receive fixed and pay floating. It gains value when the forward swap rate falls below the strike.
3) Which volatility should I use?
Use implied Black volatility quoted for the same expiry and swap tenor. If you only have historical volatility, expect pricing differences versus market quotes.
4) What does the annuity represent?
The annuity is the present-value weight of the swap’s fixed-leg payments. Many desks call it PVBP or PV01 scaling, depending on convention.
5) Should I enable the discount factor input?
Enable it only when your annuity is not already discounted to settlement. If your annuity is PVBP-style and discounted, leave it off.
6) Why is the price near intrinsic when σ is zero?
With zero volatility, the option has no uncertainty, so time value disappears. The price collapses to discounted intrinsic value based on F and K.
7) Is this suitable for American-style exercise?
No. This is a European exercise model. Bermudan or American-style swaptions need lattice, LMM, or other methods to capture early exercise.