LookbackPartialFixed

(OptionType, ModelStatistic, Asset, Strike, TimeStart, 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.

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.

TimeStart

Time, expressed in either Days or Years (depending on the TimeFormat value), until the beginning of the lookback period. Must be 0 < TimeStart < TimeExpire.

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 partial-time fixed strike lookback call option whose asset price one year from expiration is $26.75, the exercise price is $30, the time until the beginning of the lookback period is half a year, the risk-free interest rate is 6% per annum, the yield rate is 3% per annum, and the annual volatility is 30%. All of the rates are considered continuous. So,

Input

Output

Variable

Value

Function

Name

Value

OptionType

Call

1

Theoretical:

4.097199

Asset

26.75

2

Delta:

0.746008

Strike

30

3

Gamma:

0.063945

TimeStart

0.5

4

Theta:

-0.006607

TimeExpire

1

5

Implied Vol.:

0.295121

Volatility

30%

6

Vega:

0.199519

InterestRate

6%

7

Rho:

0.117137

YieldRate

3%

8

Psi:

-0.158109

MarketPrice

4

9

Lambda:

4.870578

TimeFormat

Years

11

Strike Sensitivity:

-0.528618

13

Implied Strike:

30.185527

Extreme Spread

Lookback

Fixed Strike Lookback

Partial Float Lookback

Lookback Monte Carlo