Gap

(OptionType, ModelStatistic, Asset, Strike, StrikeGap, 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.

StrikeGap

The pseudo-strike price that determines amount of the payoff. The gap is the Strike subtracted from the payoff.

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 gap call option whose asset price 180 days from expiration is $16.25, the exercise price is $15, the gap is -$4, the risk-free interest rate is 6% per annum, the yield rate is 3% per annum, and the annual volatility is 28%. All of the rates are considered continuous. So,

Input

Output

Variable

Value

Function

Name

Value

OptionType

Call

1

Theoretical:

4.579935

Asset

16.25

2

Delta:

1.159094

Strike

15

3

Gamma:

0.022085

StrikeGap

-4

4

Theta:

-0.001422

InterestRate

6%

5

Implied Vol.:

0.300434

YieldRate

3%

6

Vega:

0.008055

TimeExpire

180

7

Rho:

0.070300

Volatility

28%

8

Psi:

-0.092886

TimeFormat

Days

9

Lambda:

4.112562

MarketPrice

4.6

11

Strike Sensitivity:

-1.118509

13

Implied Strike:

14.982074

Asset or Nothing

Cash or Nothing

Two Asset Cash or Nothing

Supershare

Binary Barrier