The AveragePrice function calculates the theoretical price, sensitivities, the implied volatility, and the implied strike value of a European arithmetic or geometric average price option using either the Levy model for arithmetic or the Rubinstein model for geometric average price options. See Asian Options for a further explanation.
AveragePrice 
(OptionType, AverageType, ModelStatistic, Asset, Average, Strike, TimeToAverage, TimeExpire, Volatility, InterestRate, YieldRate, ObserveFreq, MarketPrice, 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) 
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 
Riskfree 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. 
Example
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 riskfree 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 