The Swaption function calculates the theoretical price, sensitivities, and the implied volatility of option on an interest rate swap using the Black 76 option model. See Interest Rate Models for a further explanation.
Swaption 
(SwapType, ModelStatistic, Principal, SwapTenor, TimeMaturity, Volatility, SwapRate, Frequency, TermStructure, MarketPrice, TimeFormat, RateType) 
Note: Optional arguments are shown in Italics. MarketPrice is not Optional for the Implied Volatility Calculation.
Argument 
Description 
SwapType 
Alphanumeric value indicating the type of option: •Payer = 0 or "p" (case insensitive) •Receiver = 1 or "r" (case insensitive) 
ModelStatistic 
Numeric value indicating the type of function required for the return value: •Theoretical = 1 •Delta = 2 •Gamma = 3 •Theta = 4 •ImpliedVol = 5 •Vega = 6 •Rho = 7 •Lambda = 9 
Principal 
The face value of the bond asset. Must be > 0. 
SwapTenor 
Time expressed in either Days or Years (depending on the TimeFormat value) until the maturity of the underlying swap. Must be > 0. 
TimeMaturity 
Time expressed in either Days or Years (depending on the TimeFormat value) until the maturity. Must be > 0. 
Volatility 
Annualized volatility of the underlying security. Must be > 0. 
SwapRate 
The swap rate expressed as a percentage of the principal. This rate is interpreted as a continuously compounded rate unless otherwise specified in the RateType argument. Must be > 0. 
Frequency 
Alphanumeric value indicating the coupon payment frequency when evaluation of the Swaption. 
TermStructure 
A twodimensional array or range of coupon maturity and interest rate pairs where the first column is the maturity and the second is the rate. The rates are interpreted as a continuously compounded rate unless otherwise specified in the RateType argument. All rates must be > 0.
As an example: Term Structure Coupon Rate 0.0 0.02 0.5 0.03 1.0 0.04 1.5 0.05 2.0 0.06 2.5 0.07 
MarketPrice 
Optional. The selling price of the option in the marketplace. This input is required when implied volatility and strike are calculated. Price must be > 0. 
TimeFormat 
Optional. Alphanumeric value indicating the format of the time arguments (i.e. TimeExpire, TimeExDiv, DivFrequency). If omitted, Days are used as the default. Specified as either: Days = 0 or "D" (case insensitive) Years = 1 or "Y" (case insensitive) 
RateType 
Optional. Alphanumeric value indicating the type of RateType used for both the CouponRate ad Term Structure Rate when evaluating the bond. This value is converted to Continuously Compounded for the calculations. If omitted, a continuously compounded rate is used. 
Example
Payer Swaption Valuation: Calculate the Theoretical and Gamma values of a 1½year Payer Swaption whose principal three years from maturity is $1000, the swap rate is 4.25% per annum with semi annual coupon frequency. The volatility is 20%. The coupon or term structure is as follows: 0 to 1.0 years at 2.25%, 1.0 to 2.0 years at 2.5%, 2.0 years and after at 3.0%. This means that Principal = $1000, SwapRate = 4.25%, SwapTenor = 1.5, TimeMaturity = 3, Volatility = 20%, and Frequency = SemiAnnual. All interest rates are considered continuous and the following term structure is in place:
So, 
Input 

Output 

Variable 
Value 

Function 
Name 
Value 
Swapation Type 
Payer 

1 
Theoretical: 
1.40591 
Principal 
1000 

2 
Delta (DV01): 
0.02766 
Swap Tenor 
1.5 

3 
Gamma: 
0.03553 
Time to Maturity 
3 

4 
Theta: 
0.00171 
Volatility 
20% 

5 
Implied Vol: 
0.20465 
Swap Rate 
4.25% 

6 
Vega: 
0.20007 
Frequency 
SemiAnnually 

7 
Rho (Forward Rate): 
0.01645 
Market Price 
1.50 

9 
Lambda: 
24.06016 
Time Format 
Years 










Term Structure 





Coupon 
Rate 




0.0 
2.50% 




1.0 
2.50% 




2.0 
3.00% 



