The Gap function calculates the theoretical price, sensitivities, the implied volatility, and the implied strike value of a European gap option using the Reiner and Rubinstein’s model. See Binary Options for a further explanation.
Gap 
(OptionType, ModelStatistic, Asset, Strike, StrikeGap, TimeExpire, Volatility, InterestRate, YieldRate, MarketPrice, TimeFormat, InterestType, YieldType) 
Note: Optional arguments are shown in Italics. MarketPrice is not Optional for the Implied Calculations.
Argument 
Description 
OptionType 
Alphanumeric value indicating the type of option: •Call = 1 or "c" (case insensitive) •Put = 2 or "p" (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 •StrikeSensitivity = 11 •ImpliedStrike = 13 
Asset 
The price of the underlying asset. Must be > 0. 
Strike 
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. 
StrikeGap 
The pseudostrike price that determines amount of the payoff. The gap is the Strike subtracted from the payoff. 
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. This rate is interpreted as a continuously compounded rate unless specified otherwise in the YieldType argument. 
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). If omitted, Days are used as the default. Specified as either: •Days = 0 or "D" (case insensitive) •Years = 1 or "Y" (case insensitive) 
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. 
Example
Calculate all of functions for a gap call option whose asset price 180 days from expiration is $16.25, the exercise price is $15, the gap is $4, the riskfree interest rate is 6% per annum, the yield rate is 3% per annum, and the annual volatility is 28%. All of the rates are considered continuous. So, 
Input 

Output 

Variable 
Value 

Function 
Name 
Value 
OptionType 
Call 

1 
Theoretical: 
4.579935 
Asset 
16.25 

2 
Delta: 
1.159094 
Strike 
15 

3 
Gamma: 
0.022085 
StrikeGap 
4 

4 
Theta: 
0.001422 
InterestRate 
6% 

5 
Implied Vol.: 
0.300434 
YieldRate 
3% 

6 
Vega: 
0.008055 
TimeExpire 
180 

7 
Rho: 
0.070300 
Volatility 
28% 

8 
Psi: 
0.092886 
TimeFormat 
Days 

9 
Lambda: 
4.112562 
MarketPrice 
4.6 

11 
Strike Sensitivity: 
1.118509 



13 
Implied Strike: 
14.982074 