The RollGeskeWhaleyCall function calculates the theoretical price, sensitivities, and the implied volatility of options using the RollGeskeWhaley American Call model. See Vanilla Option Models for a further explanation.
RollGeskeWhaleyCall 
(ModelStatistic, AssetPrice, StrikePrice, TimeExpire, Volatility, InterestRate, MarketPrice, TimeFormat, DivAmount, TimeExDiv, DivFrequency, InterestType) 
RollGeskeWhaleyCallDivArr 
(ModelStatistic, AssetPrice, StrikePrice, TimeExpire, Volatility, InterestRate, Dividends, MarketPrice, TimeFormat, InterestType) 
Note: Optional arguments are shown in Italics. MarketPrice is not Optional for the Implied Volatility Calculation.
Argument 
Description 
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 Note: Rho and Psi are the same •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. 
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. 
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. 
Examples
Calculate all of functions for an American call option whose asset price two years from expiration of an option is $75, the exercise price of the option is $80, the riskfree interest rate is 7% per annum, and the annual volatility is 30%. This means that AssetPrice = $75, StrikePrice = $80, InterestRate = 7%, TimeExpire = 2 years and Volatility = 30%. There are no dividends and all interest rates are considered continuous. So, 
Input 


Output 


Variable 
Value 

Function 
Name 
Value 
ExerciseType 
American 

1 
Theoretical: 
15.05605 
OptionType 
Call 

2 
Delta: 
0.65173 
Asset 
75 

3 
Gamma: 
0.01162 
Strike 
80 

4 
Theta: 
0.01454 
TimeExpire 
2 

5 
Implied Vol: 
0.08947 
Volatility 
30% 

6 
Vega: 
0.39216 
InterestRate 
7.00% 

7 
Rho: 
0.67647 
MarketPrice 
7.00 

8 
Psi: 
0.67647 
TimeFormat 
Years 

9 
Lambda: 
3.24651 



11 
Strike Sensitivity: 
0.42280 



13 
Implied Strike: 
106.26534 
Calculate all of functions for the same option as the example above, but with dividends. The first dividend is expected to occur in .5 years and with additional dividends to follow every .5 years. The dividend amount is $1 for both dividends. So, 
Input 

Output 

Variable 
Value 

Function 
Name 
Value 
ExerciseType 
American 

1 
Theoretical: 
13.13370 
OptionType 
Call 

2 
Delta: 
0.61865 
Asset 
75 

3 
Gamma: 
0.01260 
Strike 
80 

4 
Theta: 
0.01395 
TimeExpire 
2 

5 
Implied Vol: 
0.14135 
Volatility 
30% 

6 
Vega: 
0.38457 
InterestRate 
7.00% 

7 
Rho: 
0.64779 
MarketPrice 
7.00 

8 
Psi: 
0.64779 
TimeFormat 
Years 

9 
Lambda: 
3.53279 
Div Amount 
1 

11 
Strike Sensitivity: 
0.39235 
Time ExDiv 
0.5 

13 
Implied Strike: 
100.46013 
Div Frequency 
0.5 



