The BjerksundStensland function calculates the theoretical price, sensitivities, and the implied volatility of American options using the BjerksundStensland American option model. See Vanilla Option Models for a further explanation.
BjerksundStensland 
(OptionType, ModelStatistic, AssetPrice, StrikePrice, TimeExpire, Volatility, InterestRate, YieldRate, MarketPrice, TimeFormat, DivAmount, TimeExDiv, DivFrequency, DividendStyle, InterestType, YieldType) 
BjerksundStenslandDivArr 
(OptionType, ModelStatistic, AssetPrice, StrikePrice, TimeExpire, Volatility, InterestRate, YieldRate, Dividends, MarketPrice, TimeFormat, InterestType, YieldType) 
Note: Optional arguments are shown in Italics. MarketPrice is not Optional for the Implied Volatility Calculation.
Individual Models within the BjerksundStensland Model are as follow:
Black Model 
InterestRate = YieldRate 
BlackScholes Model 
YieldRate = 0 
GarmanKohlhagen Model 
YieldRate = Foreign Interest Rate 
Argument 
Description 
OptionType 
Alphanumeric value indicating the type of option: •Call = 1 or "c" (case insensitive) •Put = 2 or "p" (case insensitive) •Straddle = 3 or "s" (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 •Psi = 8 •Lambda = 9 •IntrinsicValue = 10 •StrikeSensitivity = 11 •TimeValue = 12 •Implied Strike = 13 
AssetPrice 
The price of the underlying 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. 
Volatility 
Annualized volatility of the underlying security. Must be > 0. 
InterestRate 
Riskfree interest rate expressed as a percentage. This rate is interpreted as a continuously compounded rate unless otherwise specified in the InterestType argument. Must be > 0. 
YieldRate 
Yield expressed as a percentage (dividends or interest yield) of the underlying asset price. For futures contracts, the Yield Rate is the same as the Interest Rate. This rate is interpreted as a continuously compounded rate unless specified otherwise in the YieldType argument. 
Dividends* 
A twodimensional array or range of Dividend Dates and Amount pairs where the first column is the date and the second is the amount. The Dividend Dates are a range (array) of ascending unique values. All dividend dates and amounts must both be > 0.
As an example: Dividends Date Amount 0.0 0.20 0.5 0.15 1.0 0.30 1.5 0.25 2.0 0.15 2.5 0.40
*Used for the DivArr (Dividend Array) based model only 
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) 
DivAmount 
Optional. The amount of the dividend(s). If omitted, an amount of 0 is used. Amount must be > 0. 
TimeExDiv 
Optional. The time in Days or Years until the first dividend is received. If omitted, a value of 0 is used and therefore no dividends are assessed. Value must be > 0 for dividends to be considered. 
DivFrequency 
Optional. The time in Days or Years between dividend payments. If omitted, a value of 0 is used and therefore the only dividend assessed occurs at the TimeExDiv time. The value must be > 0 for multiple dividends to be considered. 
DividendStyle 
Optional. Numeric value indicating the Style or method that dividends are handled. If omitted, the discrete cash method is used (i.e. DividendStyle = 0). •Discrete cash flow method = 0 •Continuous yield method = 1 
InterestType 
Optional. Alphanumeric value indicating the type of InterestRate to use when evaluating the option. This value is converted to Continuously Compounded for the calculations. If omitted, a continuously compounded rate is used. 
YieldType 
Optional. Alphanumeric value indicating the type of YieldRate to use when evaluating the option. This value is converted to Continuously Compounded for the calculations. If omitted, a continuously compounded rate is used. 
Examples
Calculate all of the values of an American call option whose asset price 75 days from expiration of an option is $93, the exercise price of the option is $90, the riskfree interest rate is 7.5% per annum, the yield rate is 8% per annum, and the annual volatility is 35%. This means that AssetPrice = $93, StrikePrice = $90, InterestRate = 7.5%, YieldRate = 8%, TimeExpire = 75 days and Volatility = 35%. There are no dividends and all interest rates are considered continuous. So, 
Input 

Output 

Variable 
Value 

Function 
Name 
Value 
ExerciseType 
American 

1 
Theoretical: 
7.25944 
OptionType 
Call 

2 
Delta: 
0.60344 
Asset 
93 

3 
Gamma: 
0.02593 
Strike 
90 

4 
Theta: 
0.03532 
TimeExpire 
75 

5 
Implied Vol: 
0.33370 
Volatility 
35% 

6 
Vega: 
0.15931 
InterestRate 
7.50% 

7 
Rho: 
0.08956 
YieldRate 
8.00% 

8 
Psi: 
0.10136 
MarketPrice 
7.00 

9 
Lambda: 
7.73059 
TimeFormat 
Days 

11 
Strike Sensitivity: 
0.54289 



13 
Implied Strike: 
90.48384 
Calculate all of functions for the same option as the example above, but with dividends. The first dividend is expected to occur in 30 days and the second is expected to occur in 65 days or 35 days from the first dividend. The dividend amount is $1.5 for both dividends. So, 
Input 

Output 

Variable 
Value 

Function 
Name 
Value 
ExerciseType 
American 

1 
Theoretical: 
5.58409 
OptionType 
Call 

2 
Delta: 
0.52354 
Asset 
93 

3 
Gamma: 
0.02768 
Strike 
90 

4 
Theta: 
0.03580 
TimeExpire 
75 

5 
Implied Vol: 
0.43855 
Volatility 
35% 

6 
Vega: 
0.16003 
InterestRate 
7.50% 

7 
Rho: 
0.08089 
YieldRate 
8.00% 

8 
Psi: 
0.08843 
MarketPrice 
7.00 

9 
Lambda: 
8.71933 
TimeFormat 
Days 

11 
Strike Sensitivity: 
0.46167 
Div Amount 
1.5 

13 
Implied Strike: 
87.17574 
Time ExDiv 
30 




Div Frequency 
35 




For a further example on this model see the included Excel Template located in the root directory of the addin. This example can be accessed through the Vanilla Options Template menu item after the addin has been installed properly.
A list of all of the possible Error Messages is included for convenience.