Lookback

(OptionType, ModelStatistic, Asset, 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.

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 Lookback call option whose asset price 0.5 years from expiration is $18.25, the exercise price is $18, the risk-free interest rate is 6% per annum, the yield rate is 2.5% 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:

2.994572

Asset

18.25

2

Delta:

0.212325

Strike

18

3

Gamma:

0.191744

TimeExpire

0.5

4

Theta:

-0.007750

Volatility

30%

5

Implied Vol.:

0.300620

InterestRate

6%

6

Vega:

0.087604

YieldRate

2.5%

7

Rho:

0.039332

MarketPrice

3

8

Psi:

-0.054305

TimeFormat

Years

9

Lambda:

1.293984

11

Strike Sens.:

-0.048909

13

Implied Strike:

17.906620

Extreme Spread

Fixed Strike Lookback

Partial Fixed Lookback

Partial Float Lookback

Lookback Monte Carlo