LookbackFixed

(OptionType, ModelStatistic, Asset, AssetMinMax, Strike, TimeExpire, Volatility, InterestRate, YieldRate, 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)

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.

AssetMinMax

The maximum (minimum) asset price observed in the option life time used in valuing a call (put) option. 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.

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 a fixed strike lookback call option whose asset price 225 days from expiration is $103.25, the maximum observed asset price is $105.5, the exercise price is $95, the risk-free interest rate is 6% per annum, the yield rate is 2.5% per annum, and the annual volatility is 25%. All of the rates are considered continuous. So,

Input

Output

Variable

Value

Function

Name

Value

OptionType

Call

1

Theoretical:

25.907710

Asset

103.25

2

Delta:

1.052652

AssetMinMax

105.5

3

Gamma:

0.038053

Strike

95

4

Theta:

-0.040904

TimeExpire

225

5

Implied Vol.:

0.251306

Volatility

25%

6

Vega:

0.706546

InterestRate

6%

7

Rho:

0.220245

YieldRate

2.5%

8

Psi:

-0.379950

MarketPrice

26

9

Lambda:

4.195134

TimeFormat

Days

11

Strike Sensitivity:

-0.963689

13

Implied Strike:

94.904233

Extreme Spread

Lookback

Partial Fixed Lookback

Partial Float Lookback

Lookback Monte Carlo