The BarrierLookback function calculates the theoretical price, sensitivities, the implied volatility, and the implied strike value of a European Lookback barrier option using Bermin’s model. This function evaluates upandin and upandout calls as well as downandin and downandout puts. See Barrier Options for a further explanation.
BarrierLookback 
(OptionType, ModelStatistic, Asset, Strike, Barrier, TimeBarrier, TimeExpire, Volatility, InterestRate, YieldRate, MarketPrice, Monitoring, 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: •Up_Out_Call = 1 or "uoc" (UpandOut Call) •Up_In_Call = 2 or "uic" (UpandIn Call) •Down_Out_Put = 3 or "dop" (DownandOut Put) •Down_In_Put = 4 or "dip" (DownandIn Put) 
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. 
TimeBarrier 
The expressed in either Days or Years (depending on the TimeFormat value) until the expiration of the barrier’s monitoring period. Must be 0 < TimeBarrier < TimeExpire. 
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. 
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 downandin Lookback barrier put option whose asset price 1 year from expiration is $100, the exercise price of the option is $95, the barrier is $90, the time of the barrier is 0.9 years, the riskfree interest rate is 5.5% per annum, the yield rate is 4% per annum, and the annual volatility is 20%. The barrier monitoring and all of the rates are continuous. So, 
Input 

Output 

Variable 
Value 

Function 
Name 
Value 
OptionType 
4 (DownInPut) 

1 
Theoretical: 
6.098024 
Asset 
100 

2 
Delta: 
0.409116 
Strike 
95 

3 
Gamma: 
0.020307 
Barrier 
90 

4 
Theta: 
0.008526 
TimeBarrier 
0.9 

5 
Implied Vol.: 
0.197856 
TimeExpire 
1 

6 
Vega: 
0.457244 
InterestRate 
5.5% 

7 
Rho: 
0.430754 
YieldRate 
4% 

8 
Psi: 
0.369774 
Volatility 
20% 

9 
Lambda: 
6.708991 
TimeFormat 
Years 

11 
Strike Sens.: 
0.425072 
MarketPrice 
6 

13 
Implied Strike: 
94.768669 