BarrierSingle

(OptionType, BarrierType, ModelStatistic, Asset, Strike, Barrier, Rebate, TimeExpire, Volatility, InterestRate, YieldRate, 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:

•Down_Out = 1 or "do" (Down and Out Barrier)

•Down_In = 2 or "di" (Down and In Barrier)

•Up_Out = 3 or "uo" (Up and Out Barrier)

•Up_In = 4 or "ui" (Up and In Barrier)

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.

Barrier

The barrier price level where the option is either knocked-in or knocked-out.

Rebate

The rebate paid at expiration if the barrier is hit (knock-out) or never hit (knock-in).

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.

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 down-and-out call option whose asset price 0.5 years from expiration is $55, the exercise price of the option is $50, the barrier is $53, the risk-free interest rate is 5.0% per annum, the yield rate is 2.5% per annum, and the annual volatility is 25%. The barrier monitoring is continuous, all of the rates are considered continuous and the rebate is zero. So,

Input

Output

Variable

Value

Function

Name

Value

OptionType

Call

1

Theoretical:

2.640834

BarrierType

1 (Down-and-Out)

2

Delta:

1.299502

Asset

55

3

Gamma:

-0.021202

Strike

50

4

Theta:

0.000953

Barrier

53

5

Implied Vol.:

0.167172

Rebate

0

6

Vega:

-0.029253

InterestRate

5%

7

Rho:

0.089927

YieldRate

2.5%

8

Psi:

-0.103131

TimeExpire

0.5

9

Lambda:

27.064414

Volatility

25%

11

Strike Sensitivity:

-0.158874

TimeFormat

Years

13

Implied Strike:

47.739299

MarketPrice

3

Single Barrier Trinomial

Double Barrier

Lookback Barrier

Partial Start Barrier

Partial End Barrier

Soft Barrier

Partial Two Asset Barrier

Two Asset Barrier