The OptionsMC function calculates the theoretical price of a standard European option using a Monte Carlo technique. See Vanilla Option Models for a further explanation.
OptionsMC 
(OptionType, Asset, Strike, TimeExpire, Volatility, InterestRate, YieldRate, Iterations, TimeFormat, InterestType, YieldType) 
Note: Optional arguments are shown in Italics.
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. 
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 standard European call option whose asset price 0.5 years from expiration is $60, the exercise price is $50, the riskfree interest rate is 8% per annum, the yield rate is 5.5% per annum, and the annual volatility is 20%. The number of simulation is 500. All of the rates are considered continuous. So, 
Input 

Output 

Variable 
Value 

Function Name 
Value 
Asset 
60 

Theoretical: 
10.62098 
Strike 
50 



TimeExpire 
0.5 



Volatility 
20% 



InterestRate 
8% 



YieldRate 
5.5% 



Iterations 
500 



TimeFormat 
Years 


