LookbackPartialFloat

(OptionType, ModelStatistic, Asset, Strike, Lambda, 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.

Lambda

The percentage of the strike that is fixed above or below the actual extreme.

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 the all of function of a partial-time floating strike lookback call option whose asset price 60 days from expiration is $83, the exercise price is $80, the fractional percentage of the extreme is 1, the time until the beginning of the lookback period is 30 days, the risk-free interest rate is 5% per annum, the yield rate is 4.5% 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:

7.066447

Asset

83

2

Delta:

0.345154

Strike

80

3

Gamma:

0.082245

Lambda

1

4

Theta:

-0.069281

TimeStart

30

5

Implied Vol.:

0.296676

TimeExpire

60

6

Vega

0.199974

Volatility

30%

7

Rho:

0.076726

InterestRate

5%

8

Psi:

-0.088342

YieldRate

4.5%

9

Lambda:

4.054060

MarketPrice

7

11

Strike Sensitivity:

-0.269767

TimeFormat

Days

13

Implied Strike:

80.257192

Extreme Spread

Lookback

Fixed Strike Lookback

Partial Fixed Lookback

Lookback Monte Carlo