The Rainbow function calculates the theoretical price, sensitivities, the implied volatility, the implied strike and the implied correlation value of a European style rainbow option (options on the maximum or minimum of two risky assets) using Rubinstein’s model. See Multiple Asset Options for a further explanation.
Rainbow 
(OptionType, ExtremeType, ModelStatistic, Asset1, Asset2, Strike, TimeExpire, Volatility1, Volatility2, InterestRate, YieldRate1, YieldRate2, Correlation, MarketPrice, TimeFormat, InterestType, Yield1Type, Yield2Type) 
Note: Optional arguments are shown in Italics. MarketPrice is not Optional for the Implied Calculations.
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 
Riskfree 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. 
Example
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 riskfree 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 
See Also