The BondOption function calculates the theoretical price, sensitivities, and the implied volatility of a bond option using the Black 76 model. The valuation of the bond option is done in either Cash or Quoted price. See Interest Rate Models for a further explanation.
BondOption 
(OptionType, BondPriceType, ModelStatistic, Principal, StrikePrice, TimeExpire, TimeMaturity, Volatility, CouponRate, Frequency, TermStructure, MarketPrice, TimeFormat, RateType) 
Note: Optional arguments are shown in Italics. MarketPrice is not Optional for the Implied Volatility Calculation.
Argument 
Description 
OptionType 
Alphanumeric value indicating the type of option: •Call = 1 or "c" (case insensitive) •Put = 2 or "p" (case insensitive) 
BondPriceType 
Alphanumeric value indicating the type of bond price: •Quoted Price = 0 or "q" (case insensitive) •Cash Price = 1 or "c" (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 •StrikeSensitivity = 11 •Implied Strike = 13 
Principal 
The face value of the bond asset. Must be > 0. 
StrikePrice 
The price at which the asset can be purchased if the option is a call or sold if the option is a put. Must be > 0. 
TimeExpire 
Time expressed in either Days or Years (depending on the TimeFormat value) until the options expiration. Must be > 0. 
TimeMaturity 
Time expressed in either Days or Years (depending on the TimeFormat value) until the bond maturity. Must be > 0. 
Volatility 
Annualized volatility of the underlying security. Must be > 0. 
CouponRate 
The annual coupon 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 the bond. 
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
Quoted Bond Option ValuationCalculate the Quoted Theoretical and Gamma values of a Bond 3 month Call Option whose principal two years from maturity is $100, the strike price is $98, the coupon rate is 5.5% per annum with semi annual coupon frequency. The volatility is 25%. The coupon or term structure is as follows: 0 to 1.0 years at 2.5%, 1.0 to 2.0 years at 3.0%, 2.0 years and after at 3.5%. This means that Principal = $100, Strike = $98, CouponRate = 5.5%, TimeExpiration = 0.25, TimeMaturity = 2, Volatility = 25%, and CouponFrequency = SemiAnnual. All interest rates are considered continuous and the following term structure is in place:
So, 
Input 

Output 

Variable 
Value 

Function 
Name 
Value 
OptionType 
Call 

1 
Theoretical: 
5.071338 
Bond Price Type 
Quoted Price 

2 
Delta: 
0.017488 
Principal 
100 

3 
Gamma: 
0.000386 
Strike 
98 

4 
Theta: 
0.005112 
Time to Expiration 
0.25 

5 
Implied Vol: 
2.277873 
Time to Maturity 
2.00 

6 
Vega: 
0.000000 
Coupon Rate 
5.5 

7 
Rho: 
1.671079 
Frequency 
SemiAnnually 

9 
Lambda: 
20.197888 
Market Price 
6.00 

11 
Strike Sens: 
0.993459 
Time Format 
Years 

13 
Implied Strike: 
97.065224 






Term Structure 





Coupon 
Rate 




0.0 
2.50% 




1.0 
3.00% 




2.0 
3.50% 



