BarrierDouble

(OptionType, BarrierType, ModelStatistic, Asset, Strike, LowerBarrier, UpperBarrier, TimeExpire, Volatility, InterestRate, YieldRate, LowCurve, UpCurve, MarketPrice, Monitoring, 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)

BarrierType

Alphanumeric value indicating the barrier type:

•Knock_In = 1 or "ki" (case insensitive)

•Knock_Out = 2 or "ko" (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.

LowerBarrier

The lower barrier price level.

UpperBarrier

The upper barrier price level.

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.

LowCurve

Optional. The growth or curvature of the lower barrier. If omitted, a 0 (zero) is used.

UpCurve

Optional. The growth or curvature of the upper barrier. If omitted, a 0 (zero) is used.

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.

Monitoring

Optional. Alphanumeric value indicating the frequency of the barrier monitoring. If omitted, a ContinuousSample is used.

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 knock-out call option whose asset price 117 days from expiration is $100, the exercise price of the option is $90, the lower barrier is $80, the upper barrier is $120, the risk-free interest rate is 6% per annum, the yield rate is 5% per annum, and the annual volatility is 25%. The barrier monitoring and all of the rates are continuous. So,

Input

Output

Variable

Value

Function

Name

Value

OptionType

Call

1

Theoretical:

6.273983

BarrierType

2 (Knock-Out)

2

Delta:

0.089901

Asset

100

3

Gamma:

-0.042287

Strike

90

4

Theta:

0.036990

LowerBarrier

80

5

Implied Vol.:

0.258107

UpperBarrier

120

6

Vega:

-0.341438

InterestRate

6%

7

Rho:

0.040682

YieldRate

5%

8

Psi:

-0.060794

TimeExpire

117

9

Lambda:

1.432919

Volatility

25%

11

Strike Sensitivity:

-0.552753

TimeFormat

Days

13

Implied Strike:

90.500763

MarketPrice

6

Single Barrier

Single Barrier Trinomial

Lookback Barrier

Partial Start Barrier

Partial End Barrier

Soft Barrier

Partial Two Asset Barrier

Two Asset Barrier