Asian Monte Carlo Function

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Asian Monte Carlo Function

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The AsianMC function calculates the theoretical price of a European average price Asian option using either an Antithetic or Control Variate Monte Carlo technique. See Asian Options for a further explanation.

 

 

AsianMC

(OptionType, VariateType, 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)

VariateType

Alphanumeric value indicating the Variate type or model:

Antithetic = 1 or "a" (case insensitive)

Control = 2 or "c" (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 an average price call option whose asset price 0.5 years from expiration is $55.75, the exercise price is $60, the risk-free interest rate is 6% per annum, the yield rate is 4% per annum, and the annual volatility is 25%. 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 Name

Antithetic

Control

Asset

55.75

 

Theoretical:

0.85765

0.86939

Strike

60

 

 

 

 

TimeExpire

0.5

 

 

 

 

Volatility

25%

 

 

 

 

InterestRate

6%

 

 

 

 

YieldRate

4%

 

 

 

 

NumSteps

100

 

 

 

 

Iterations

100

 

 

 

 

TimeFormat

Years

 

 

 

 

 

 

See Also

Average Price

Average Strike

Asian Spread Monte Carlo

 

 

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 Asian Template menu item after the add-in has been installed properly.

 

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