AveragePrice

(OptionType, AverageType, ModelStatistic, Asset, Average, Strike, TimeToAverage, 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.

Average

The geometric mean of the asset price over the monitoring period that was contracted.

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.

TimeToAverage

The time to the start of the averaging period. A positive value means that the averaging will begin in the future, a negative value means that the averaging began prior to the current date, and a zero value means that the averaging period begins today. The value is expressed in either Days or Years depending on the TimeFormat value.

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 price call option whose asset price 1 year from expiration is $49, the exercise price of the option is $50, the average price sampled continuously is $51, the risk-free interest rate is 6% per annum, the yield rate is 7.51% per annum, and the annual volatility is 30%. The averaging period begins today and all of the rates are considered continuous. So,

Input    

Output

Variable

Value

Function

Name

Geometric

Arithmetic

OptionType

Call

1

Theoretical:

2.443600

2.607817

Asset

49

2

Delta:

0.420669

0.440108

Strike

51

3

Gamma:

0.043319

0.043754

Average

50

4

Theta:

-0.003022

-0.003474

InterestRate

6%

5

Implied Vol.:

0.360143

0.336843

YieldRate

7.51%

6

Vega:

0.093681

0.106197

TimeToAverage

0

7

Rho:

0.078628

0.085430

TimeExpire

1

8

Psi:

-0.103064

-0.111509

Volatility

30.0%

9

Lambda:

8.435406

8.269477

TimeFormat

Years

11

Strike Sens.:

-0.363383

-0.379149

MarketPrice

3

13

Implied Strike:

48.58600

49.01968

Average Strike

Asian Monte Carlo

Asian Spread Monte Carlo