AsianSpreadMC

(OptionType, Asset1, Asset2, Strike, TimeExpire, Volatility1, Volatility2, InterestRate, YieldRate1, YieldRate2, Correlation, NumSteps, Iterations, TimeFormat, InterestType, YieldRate1Type, YieldRate2Type)

Argument

Description

OptionType

Alphanumeric value indicating the type of option:

•Call = 1 or "c" (case insensitive)

•Put = 2 or "p" (case insensitive)

Asset1

The price of the first underlying asset. Must be > 0.

Asset2

The price of the second 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.

Volatility1

Annualized volatility of the first underlying security.

Must be > 0.

Volatility2

Annualized volatility of the second 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.

YieldRate1

Yield, expressed as a percentage (dividends or interest yield), of the first underlying asset price. This rate is interpreted as a continuously compounded rate unless specified otherwise in the YieldRate1Type argument.

YieldRate2

Yield, expressed as a percentage (dividends or interest yield), of the second underlying asset price. This rate is interpreted as a continuously compounded rate unless specified otherwise in the YieldRate2Type argument.

Correlation

The correlation between the first underlying asset price and the second underlying asset price.

Must be -1 < Correlation < 1.

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.

YieldRate1Type

Optional. Alphanumeric value indicating the type of YieldRate1 to use when evaluating the option. This value is converted to Continuously Compounded for the calculations. If omitted, a Continuously Compounded rate is used.

YieldRate2Type

Optional. Alphanumeric value indicating the type of YieldRate2 to use when evaluating the option. This value is converted to Continuously Compounded for the calculations. If omitted, a Continuously Compounded rate is used.

Using Monte Carlo Simulation, calculate the Theoretical value of a Two-Asset Asian spread option call option where the option is 225 days from expiration, the first asset price is $25.50, the second asset price is $26, the exercise price is $3.25, the risk-free interest rate is 8% per annum, the yield rate of the first asset is 6% per annum, the yield rate of the second asset is 4% per annum, the annual volatility of the first asset is 20%, the annual volatility of the second asset is 25%, and the correlation is 0.5. The number of simulation is 100 and the number of simulations per day is 100. All rates are considered continuous. So,

Input

Output

Variable

Value

Function Name

Value

Asset1

25.5

Theoretical:

0.06246

Asset2

26

Strike

3.25

TimeExpire

225

Volatility1

20%

Volatility2

25%

InterestRate

8%

YieldRate1

6%

YieldRate2

4%

Correlation

0.5

NumSteps

100

Iterations

100

TimeFormat

Days

Average Price

Average Strike

Asian Monte Carlo