Rainbow

(OptionType, ExtremeType, ModelStatistic, Asset1, Asset2, Strike, TimeExpire, Volatility1, Volatility2, InterestRate, YieldRate1, YieldRate2, Correlation, MarketPrice, TimeFormat, InterestType, Yield1Type, Yield2Type)

Argument

Description

OptionType

Alphanumeric value indicating the type of option:

•Call = 1 or "c" (case insensitive)

•Put = 2 or "p" (case insensitive)

ExtremeType

Alphanumeric value indicating the barrier type:

•MaxAsset = 1 or "max" (case insensitive)

•MinAsset = 2 or "min" (case insensitive)

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

•ImpliedCorrelation = 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.

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 Yield1Type 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 Yield2Type 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.

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.

Yield1Type

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.

Yield2Type

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 rainbow call on the maximum of two assets where the option is 60 days from expiration. The first asset price is $32, the second asset price is $38, the exercise price is $35, the risk-free interest rate is 6.0% per annum, yield rate of the first and second assets are both 4% per annum, the correlation is 0.25, the annual volatility of the first asset is 20%, and the annual volatility of the second asset is 30%. The interest rates are considered continuous. So,

Input

Output

Variable

Value

Function

Name

Value

OptionType

Call

1

Theoretical:

3.758206

ExtremeType

1 (MaxAsset)

4

Theta:

-0.013926

Asset1:

32

7

Rho:

0.043225

Asset2:

38

11

Strike Sensitivity:

-0.751292

Strike:

35

13

Implied Strike:

35.010930

TimeExpire

60

30

Delta Asset 1:

0.036148

Volatility1:

20%

31

Delta Asset 2:

0.760439

Volatility2:

30%

32

Gamma 1:

0.027726

InterestRate

6%

33

Gamma 2:

0.066598

YieldRate1:

4%

34

Implied Vol. 1:

0.188753

YieldRate2:

4%

35

Implied Vol. 2:

0.298229

Correlation:

0.25

36

Vega Vol. 1:

0.007789

MarketPrice:

3.75

37

Vega Vol. 2:

0.046395

TimeFormat

Days

38

Psi Yield 1:

-0.001901

39

Psi Yield 2:

-0.047501

42

Lambda 1:

0.307785

43

Lambda 2:

7.688961

48

Chi:

-0.123509

50

Implied Corr:

0.318976

Dual Strike

Exchange

Exchange Binomial

Exchange on Exchange

Portfolio

Rainbow Binomial

Spread

Spread Binomial

Two Asset Correlation