The BarrierSingleTri function calculates the theoretical price, sensitivities, the implied volatility, and the implied strike value of an American or European style single barrier option a trinomial lattice model. This function evaluates upandin, downandin, upandout, and downandout barrier options for both calls and puts. See Barrier Options for a further explanation.
BarrierSingleTri 
(ExerciseType, OptionType, BarrierType, ModelStatistic, Asset, Strike, Barrier, Rebate, TimeExpire, Volatility, InterestRate, YieldRate, Iterations, MarketPrice, TimeFormat, InterestType, YieldType) 
Note: Optional arguments are shown in Italics. MarketPrice is not Optional for the Implied Calculations.
Argument 
Description 
ExerciseType 
Alphanumeric value indicating the exercise type: •American = 0 or "a" (case insensitive) •European = 1 or "e" (case insensitive) 
OptionType 
Alphanumeric value indicating the type of option: •Call = 1 or "c" (case insensitive) •Put = 2 or "p" (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) 
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. 
Rebate 
The rebate paid at expiration if the barrier is hit (knockout). The rebate is used only on knockedout options. 
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. 
Iterations 
The number of iterations used for the trinomial model. Must be between 5 and 500. 
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 upandout American call option whose asset price 0.5 years from expiration is $55, the exercise price of the option is $50, the barrier is $60, the riskfree interest rate is 5.0% per annum, the yield rate is 2.5% per annum, and the annual volatility is 25%. There is no rebate, Iterations = 200 and all of the rates are considered continuous. So, 
Input 

Output 

Variable 
Value 

Function 
Name 
Value 
ExerciseType 
American 

1 
Theoretical: 
6.484380 
OptionType 
Call 

2 
Delta: 
0.627804 
BarrierType 
3 (UpandOut) 

3 
Gamma: 
0.012876 
Asset 
55 

4 
Theta: 
0.004802 
Strike 
50 

5 
Implied Vol.: 
0.172500 
Barrier 
60 

6 
Vega: 
0.059755 
Rebate 
0 

7 
Rho: 
0.061800 
InterestRate 
5% 

8 
Psi: 
0.071870 
YieldRate 
2.5% 

9 
Lambda: 
5.324984 
TimeExpire 
0.5 

11 
Strike Sensitivity: 
0.778997 
Volatility 
25% 

13 
Implied Strike: 
50.625794 
TimeFormat 
Years 




Iterations 
200 




MarketPrice 
6 



