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	Risk-free 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 risk-free 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

Remark

For a further example on this model see the included Excel Template located in the root directory of the add-in. This example can be accessed through the Lookback Template menu item after the add-in has been installed properly.

A list of all of the possible Error Messages is included for convenience.

Lookback Monte Carlo Function

Lookback Monte Carlo Function

See Also

Remark