BarrierTwoAsset

(OptionType, BarrierType, ModelStatistic, Asset1, Asset2, Strike, Barrier, TimeExpire, Volatility1, Volatility 2, InterestRate, YieldRate1, YieldRate2, Correlation, MarketPrice, Monitoring, TimeFormat, InterestType, YieldRate1Type, YieldRate2Type)

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

•Theta = 4

•Rho = 7

•StrikeSensitivity = 11

•ImpliedStrike = 13

•Delta1 = 30

•Delta2 = 31

•Gamma1 = 32

•Gamma2 = 33

•ImpliedVol1 = 34

•ImpliedVol2 = 35

•Vega1 = 36

•Vega2 = 37

•Psi1 = 38

•Psi2 = 39

•Lambda1 = 42

•Lambda2 = 43

•Chi = 48

•ImpliedCorr = 50

Asset1

The price of the underlying asset one. Must be > 0.

Asset2

The price of the underlying asset two. 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.

TimeExpire

Time, expressed in either Days or Years (depending on the TimeFormat value), until the options expiration. Must be > 0.

Volatility1

Annualized volatility of the asset one. Must be > 0.

Volatility2

Annualized volatility of the asset two. 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.

YieldRate1

Yield, expressed as a percentage (dividends or interest yield), of the first underlying asset price. This rate is interpreted as a continuously compounded rate unless specified otherwise in the YieldRate1Type argument.

YieldRate2

Yield, expressed as a percentage (dividends or interest yield), of the second underlying asset price. This rate is interpreted as a continuously compounded rate unless specified otherwise in the YieldRate2Type argument.

Correlation

The correlation between the first underlying asset price and the second underlying asset price.

Must be -1 < Correlation < 1.

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.

YieldRate1Type

Optional. Alphanumeric value indicating the type of YieldRate1 to use when evaluating the option. This value is converted to Continuously Compounded for the calculations. If omitted, a Continuously Compounded rate is used.

YieldRate2Type

Optional. Alphanumeric value indicating the type of YieldRate2 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-In two-asset call where the option is 180 days from expiration, the first asset price is $55, the second asset price is $48, the exercise price is $53, the barrier is $50, the risk-free interest rate is 6% per annum, yield rate of the first and second assets are both 3.5% per annum, the correlation is 0.4, the annual volatility of the first asset is 30%, and the annual volatility of the second asset is 25%. The barrier monitoring and all of the rates are continuous. So,

Input

Output

Variable

Value

Function

Name

Value

OptionType

Call

1

Theoretical:

7.817481

BarrierType

1 (Down-and-In)

4

Theta:

-0.012230

Asset1:

55

7

Rho:

0.246784

Asset2:

48

11

Strike Sensitivity:

-0.670581

Strike:

53

13

Implied Strike:

52.729955

Barrier:

50

30

Delta Asset 1:

0.788333

TimeExpire

180

31

Delta Asset 2:

-1.083260

Volatility1:

30%

32

Gamma 1:

0.036469

Volatility2:

25%

33

Gamma 2:

0.098767

InterestRate

6%

34

Implied Volatility 1:

0.309173

YieldRate1:

3.5%

35

Implied Volatility 2:

0.233354

YieldRate2:

3.5%

36

Vega Volatility 1:

0.198789

Correlation:

0.4

37

Vega Volatility 2:

-0.100995

MarketPrice:

8

38

Psi Yield 1:

-0.213822

TimeFormat

Years

39

Psi Yield 2:

-0.071514

32

Lambda 1:

5.546325

42

Lambda 2:

-6.651308

48

Chi:

2.668645

50

Implied Correlation:

0.466836

Single Barrier

Single Barrier Trinomial

Double Barrier

Lookback Barrier

Partial Start Barrier

Partial End Barrier

Soft Barrier

Two Asset Barrier