The BinaryBarrier function calculates the theoretical price, sensitivities, the implied volatility, and the implied strike value of all 28 different types of European binary barrier options using Reiner and Rubinstein’s model. See Binary Options for a further explanation.
BinaryBarrier 
(OptionType, BarrierType, PayoutType, ModelStatistic, Asset, Strike, Barrier, Payout, TimeExpire, Volatility, InterestRate, YieldRate, MarketPrice, Monitoring, TimePayout, 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) •Both = 4 or "b" (case insensitive) 
BarrierType 
Alphanumeric value indicating the barrier type: •Down_Out = 1 or "do" (Down and Out Barrier) •Down_In = 2 or "di" (Down and In Barrier) •Up_Out = 3 or "uo" (Up and Out Barrier) •Up_In = 4 or "ui" (Up and In Barrier) 
PayoutType 
Alphanumeric value indicating the type of payout: •Cash_Nothing = 1 or "cn" (case insensitive) •Asset_Nothing = 2 or "an" (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. 
Barrier 
The barrier price level where the option is either knockedin or knockedout. 
Payout 
The pay out depending on whether the asset price has hit the barrier or not. 
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. 
Monitoring 
Optional. Alphanumeric value indicating the frequency of the barrier monitoring. If omitted, a ContinuousSample is used. 
TimePayout 
Optional. Alphanumeric value indicating the when the payout occurs. This parameter is only considered when the OptionType is set to both and the Barrier Type is either Up_In or Down_In. For Down_Out and Up_Out Barriers when TimePayout is set to A_Hit, zero is returned. If omitted, At_Expiration is used as the default. Specified as either: •At_Expiration = 0 or "ae" (case insensitive) •At_Hit = 1 or "at" (case insensitive) 
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 upandin asset or nothing call option whose asset price 35 days from expiration is $90, the exercise price of the option is $100, the barrier is $92, the rebate is $5, the riskfree interest rate is 8% per annum, the yield rate is 5% per annum, and the annual volatility is 20%. The barrier monitoring is continuous and all of the rates are considered continuous. So, 
Input 

Output 

Variable 
Value 

Function 
Name 
Value 
OptionType 
Call 

1 
Theoretical: 
4.676320 
BarrierType 
4 (UpandIn) 

2 
Delta: 
1.767302 
PayoffType 
0 (AssetorNothing) 

3 
Gamma: 
0.518776 
Asset 
90 

4 
Theta: 
0.242300 
Strike 
100 

5 
Implied Vol.: 
0.203987 
Barrier 
92 

6 
Vega: 
0.805880 
Rebate 
5 

7 
Rho: 
0.148036 
InterestRate 
8% 

8 
Psi: 
0.152521 
YieldRate 
5% 

9 
Lambda: 
34.013316 
TimeExpire 
35 

11 
Strike Sensitivity: 
1.543808 
Volatility 
20% 

13 
Implied Strike: 
99.796068 
TimeFormat 
Days 




MarketPrice 
5 



