AverageStrike

(OptionType, AverageType, ModelStatistic, Asset, TimeExpire, Volatility, InterestRate, YieldRate, ObserveFreq, MarketPrice, TimeFormat, InterestType, YieldType)

Argument

Description

OptionType

Alphanumeric value indicating the type of option:

•Call = 1 or "c" (case insensitive)

•Put = 2 or "p" (case insensitive)

AverageType

Alphanumeric value indicating the Average type or model:

•Geometric = 1 or "g" (case insensitive)

•Arithmetic = 2 or "a" (case insensitive)

ModelStatistic

Numeric value indicating the type of function required for the return value:

•Theoretical = 1

•Delta = 2

•Gamma = 3

•Theta = 4

•ImpliedVol = 5

•Vega = 6

•Rho = 7

•Psi = 8

•Lambda = 9

•StrikeSensitivity = 11

•ImpliedStrike = 13

Asset

The price of the underlying asset. 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.

ObserveFreq

Optional. The frequency of the observations while collecting the AveragePrice. Note: only applied to the Geometric Average. If omitted, ContinuousSample is used as the default.

MarketPrice

Optional. The selling price of the option in the marketplace. This input is required when implied volatility and strike are calculated. Price must be > 0.

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.

Calculate all of functions for an average strike call option whose asset price 0.75 years from expiration is $25, the risk-free interest rate is 5.0% per annum, the yield rate is 3.0% per annum, and the annual volatility is 20%. All of the rates are considered continuous. So,

Input

Output

Variable

Value

Function

Name

Geometric

Arithmetic

OptionType

Call

1

Theoretical:

1.096360

1.064409

Asset

25

2

Delta:

0.043854

0.042576

InterestRate

5%

3

Gamma:

0.000000

0.000000

YieldRate

3%

4

Theta:

-0.002131

-0.002015

TimeExpire

0.75

5

Implied Vol.:

0.181187

0.186707

Volatility

20%

6

Vega:

0.051359

0.066625

TimeFormat

Years

7

Rho:

0.044804

0.043088

MarketPrice

1

8

Psi:

-0.051558

-0.049659

9

Lambda:

1.000000

1.000000

Average Price

Asian Monte Carlo

Asian Spread Monte Carlo