BarrierPartialStart

(OptionType, BarrierType, ModelStatistic, Asset, Strike, Barrier, TimeBarrier, 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.

TimeBarrier

The expressed in either Days or Years (depending on the TimeFormat value) until the expiration of the barrier’s monitoring period. Must be 0 < TimeBarrier < 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.

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 partial-start barrier call option whose asset price 1 year from expiration is $53, the exercise price of the option is $55, the barrier is $48, the time of the barrier is 0.25 years, the risk-free interest rate is 6% per annum, the yield rate is 4% per annum, and the annual volatility is 30%. The barrier monitoring and all of the rates are continuous. So,

Input

Output

Variable

Value

Function

Name

Value

OptionType

Call

1

Theoretical:

4.066680

BarrierType

1 (Down-and-Out)

2

Delta:

0.788770

Asset

53

3

Gamma:

-0.009459

Strike

55

4

Theta:

0.001653

Barrier

48

5

Implied Vol.:

0.289722

TimeBarrier

0.25

6

Vega:

0.062999

TimeExpire

1

7

Rho:

0.165148

InterestRate

6%

8

Psi:

-0.205815

YieldRate

4%

9

Lambda:

10.279839

Volatility

30%

11

Strike Sens.:

-0.251698

TimeFormat

Years

13

Implied Strike:

55.266548

MarketPrice

4

Single Barrier

Single Barrier Trinomial

Double Barrier

Lookback Barrier

Partial End Barrier

Soft Barrier

Partial Two Asset Barrier

Two Asset Barrier