The BarrierTwoAsset function calculates the theoretical price, sensitivities, the implied volatility, the implied strike and the implied correlation value of a European twoasset barrier option using Heynen and Kat’s model. This function evaluates upandin, downandin, upandout, and downandout barrier options for both calls and puts. See Barrier Options for a further explanation.
BarrierTwoAsset 
(OptionType, BarrierType, ModelStatistic, Asset1, Asset2, Strike, Barrier, TimeExpire, Volatility1, Volatility 2, InterestRate, YieldRate1, YieldRate2, Correlation, MarketPrice, Monitoring, TimeFormat, InterestType, YieldRate1Type, YieldRate2Type) 
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) 
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 
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 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. 
Example
Calculate all of functions for a downandIn twoasset 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 riskfree 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 (DownandIn) 

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 