The LookbackMC function calculates the theoretical price of a European floating strike lookback option using either an Antithetic or Control Variate Monte Carlo technique. See Lookback Options for a further explanation.
LookbackMC 
(OptionType, Asset, Strike, TimeExpire, Volatility, InterestRate, YieldRate, NumSteps, Iterations, 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) 
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. 
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. 
NumSteps 
The number of steps per simulation (or samples per day). Must be between 1 and 1000. 
Iterations 
The number of Monte Carlo simulations or trials. Must be between 1and 5000. 
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
Using Monte Carlo Simulation, calculate the theoretical value of a floating strike lookback call option whose asset price 0.5 years from expiration is $100, the exercise price is $110, the riskfree interest rate is 5% per annum, the yield rate is 3% per annum, and the annual volatility is 30%. The number of simulation is 100 and the number of simulations per day is 100. All of the rates are considered continuous. So, 
Input 

Output 

Variable 
Value 

Function 
Value 
OptionType 
Call 

Theoretical: 
16.286577 
Asset 
100 



Strike 
110 



TimeExpire 
0.5 



Volatility 
30% 



InterestRate 
5% 



YieldRate 
3% 



Iterations 
100 



NumSteps 
100 



TimeFormat 
Years 


