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 |
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Output |
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Variable |
Value |
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Function Name |
Antithetic |
Control |
Asset |
55.75 |
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Theoretical: |
0.85765 |
0.86939 |
Strike |
60 |
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TimeExpire |
0.5 |
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Volatility |
25% |
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InterestRate |
6% |
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YieldRate |
4% |
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NumSteps |
100 |
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Iterations |
100 |
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TimeFormat |
Years |
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