DoubleBarrier





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A double barrier option is knocked in or out if the underlying price touches a lower boundary L or upper boundary U prior to expiration.

CO=Call up-and-out-down-and-out, PO=Put up-and-out-down-and-out, CI=Call up-and-in-down-and-in, PI=Put up-and-in-down-and-in. Alpha1 and Alpha2 determine the curvature of the lower L and Upper U absorbing boundaries.

When both are equal to 0, we have two flat boundaries.

Where Alpha1 is less than 0 and Alpha2 is greater than 0 we have a lower boundary exponentially growing as time elapses, while the upper boundary will be exponentially decaying.

An Alpha1 greater than 0 and Alpha2 less than 0 corresponds to a convex downward lower boundary and a convex upward upper boundary.

This function utilizes an analytical (closed-form) algorithm.

Note that the risk (greek) numbers produced are the mathematically defined equivalent of a derivative (instantaneous change).

You can convert the risk number to your own definition of risk by multiplying by the shift you require.

For example, for a typical definition of VANNA, (change in underlying and volatility), where one defines the change in the underlying as a single unit of change (1.0) and the change in volatility as a one percent change (0.01), simply multiply the VANNA result calculated by (1.0*0.01).

For VEGA, change in volatility of one percent (0.01), simply multiply the VEGA result by 0.01. Within option contracts THETA is negative, however the mathematically defined equivalent of THETA (instantaneous FORWARD change in time) is positive.

Internally we have negated this value for you.

To express THETA as THETA per day, simply multiply the THETA result by 1/365 or 1/252 (depending on whether you require calendar days or business days).



Note: Within Excel, the function is named - CT.EXO.DoubleBarrier




High level graphic of DoubleBarrier() function with parameters. Blue square node is the actual function with the parameters ordered.



Parameter Description


  1. ValueDate parameter

    Valuation Date (typically equal to Today's date)
  2. dayCounter parameter

    For any input parameter within this function that represents a dividend rate, risk free rate, foreign rate or holding cost rate, these rates will be defined as annually compounded using the DayCounter defined within this parameter. Thus if 'actual365' is used for this 'dayCounter' parameter, then all input parameters that represent a dividend, risk free, foreign or holding cost rates will be defined as annually compounded Actual365 rates.
  3. DblBarrier parameter

    Option Types CO, PO, CI, PI
  4. Underlying parameter

    Underlying price
  5. X parameter

    Strike price of the option
  6. L parameter

    Continuous Lower barrier level
  7. U parameter

    Continuous Upper barrier level
  8. AdjBarrFreqL parameter

    Monitoring frequency that you wish the continuous lower barrier level value entered to have. (Basically will convert the barrier from continuous to discrete. If you choose 'Continuously', the barrier will still be a Continuous barrier). Valid values are : Continuously, Hourly, Daily, Weekly or Monthly.
  9. AdjBarrFreqU parameter

    Monitoring frequency that you wish the continuous upper barrier level value entered to have. (Basically will convert the barrier from continuous to discrete. If you choose 'Continuously', the barrier will still be a Continuous barrier). Valid values are : Continuously, Hourly, Daily, Weekly or Monthly.
  10. Time parameter

    Time to option maturity.
  11. Rate parameter

    For the underlying (equity, futures, FX or commodity), this should be an annualised rate (risk free rate or foreign rate). If this is an option on a FX underlying, then if the underlying is quoted as domestic/foreign then this rate will be the domestic rate. If, however, the FX underlying is quoted as foreign/domestic then this will be the foreign rate.
  12. B parameter

    For the underlying (equity, futures, FX or commodity), this should be an annualised rate (dividend rate, risk free rate, foreign rate or holding cost rate respectively). If this is an option on a FX underlying, then if the underlying is quoted as domestic/foreign then this rate will be the foreign rate. If, however, the FX underlying is quoted as foreign/domestic then this will be the domestic rate.
  13. Vol parameter

    Volatility of the underlying.
  14. Delta1 parameter

    Controls the curvature of the Lower L and upper U barriers.
  15. Delta2 parameter

    Controls the curvature of the Lower L and upper U barriers.
  16. Greek parameter

    For the option premium specify 'PREMIUM'. For all first derivatives, you can specify one of the following : 'dUnderlying' (for the 'Underlying' parameter), 'dX' (for the 'X' parameter), 'dL' (for the 'L' parameter), 'dU' (for the 'U' parameter), 'dTime' (for the 'Time' parameter), 'dRate' (for the 'Rate' parameter), 'dB' (for the 'B' parameter), 'dVol' (for the 'Vol' parameter), 'dDelta1' (for the 'Delta1' parameter), 'dDelta2' (for the 'Delta2' parameter), For second order derivatives, you can specify combinations of the first order derivatives (i.e. - 'dUnderlyingdUnderlying', 'dVoldVol', 'dUnderlyingdVol'. )


Extended information

Function Syntax

VB Syntax


Double CTExoticOptions.DoubleBarrier( _
Long ValueDate, _
DayCountEnum dayCounter, _
String DblBarrier, _
Double Underlying, _
Double X, _
Double L, _
Double U, _
String AdjBarrFreqL, _
String AdjBarrFreqU, _
Long Time, _
Double Rate, _
Double B, _
Double Vol, _
Double Delta1, _
Double Delta2, _
String Greek)


Excel Spreadsheet Syntax


=CT.EXO.DoubleBarrier(
Excel Numeric Cell ValueDate,
Excel String Cell dayCounter,
Excel String Cell DblBarrier,
Excel Numeric Cell Underlying,
Excel Numeric Cell X,
Excel Numeric Cell L,
Excel Numeric Cell U,
Excel String Cell AdjBarrFreqL,
Excel String Cell AdjBarrFreqU,
Excel Numeric Cell Time,
Excel Numeric Cell Rate,
Excel Numeric Cell B,
Excel Numeric Cell Vol,
Excel Numeric Cell Delta1,
Excel Numeric Cell Delta2,
Excel String Cell Greek)


C++ Syntax


static double DoubleBarrier(
long ValueDate,
DayCountEnum dayCounter,
std::string DblBarrier,
double Underlying,
double X,
double L,
double U,
std::string AdjBarrFreqL,
std::string AdjBarrFreqU,
long Time,
double Rate,
double B,
double Vol,
double Delta1,
double Delta2,
std::string Greek);


DotNET Syntax


System.Double CTExoticOptionsSA.DoubleBarrier(
System.Int32 ValueDate,
CTIEnums.DayCountEnum dayCounter,
System.String DblBarrier,
System.Double Underlying,
System.Double X,
System.Double L,
System.Double U,
System.String AdjBarrFreqL,
System.String AdjBarrFreqU,
System.Int32 Time,
System.Double Rate,
System.Double B,
System.Double Vol,
System.Double Delta1,
System.Double Delta2,
System.String Greek);

Parameter data types

ArgNameArgTypeIsKey
ValueDateLongFALSE
dayCounterDayCountEnumFALSE
DblBarrierStringFALSE
UnderlyingDoubleFALSE
XDoubleFALSE
LDoubleFALSE
UDoubleFALSE
AdjBarrFreqLStringFALSE
AdjBarrFreqUStringFALSE
TimeLongFALSE
RateDoubleFALSE
BDoubleFALSE
VolDoubleFALSE
Delta1DoubleFALSE
Delta2DoubleFALSE
GreekStringFALSE


Example Inputs

The first column represents the name of the parameters. The second column specifies whether the parameters are optional or not. Finally the last column provides some sample input data.
Function call input string-keys are always in the format : "NAME.EXTTAG.TICKER" The "EXTTAG.TICKER" part is determined from the output of other, capetools, object creation functions.


ArgNameIsOptional (Excel only)Example
ValueDateFALSE19/Jul/2005 (serial date type)
dayCounterFALSEACT365
DblBarrierFALSECO
UnderlyingFALSE100
XFALSE100
LFALSE90
UFALSE105
AdjBarrFreqLFALSEDaily
AdjBarrFreqUFALSEDaily
TimeFALSE18/Oct/2005 (serial date type)
RateFALSE0.1
BFALSE0.00
VolFALSE0.25
Delta1FALSE0
Delta2FALSE0
GreekFALSEPREMIUM


Example function usage


The C# example below contains all the sub-function calls leading up to this function call. As a result, the example can contain a lot of code.

The VB.NET, J#, C++.NET, Java, Excel VBA, Visual Basic 6 (via COM) and C++ examples below contain function code stubs for the calls leading up to this function call. However, the function call for this function is displayed.
You can easily reproduce the stub functions code from the C# example.


If you are accessing this functrion via the MiniXL libraries, this function is present within the CT.QL.Pricing20 MiniXL Excel Addin.

Within our Excel Example Addin Generator, we have used the following QuantTools sub-functions in order to prepare the arguments needed to call the DoubleBarrier() function. If you are executing this function via the MiniXL libraries, the module addin name, (in brackets, to the right of the sub-functions listed below), indicates the MiniXL library in which the sub-function is held. You will need to load this library into your Excel session (along with any other libraries that the sub-function call within the addin requires (ie - CT.QT.Utils20 addin in almost all cases) in order for the example to compute successfully.


The following four examples demostrate calling this function within a Microsoft .NET environment

The following four examples demostrate calling this function within a non .NET environment

The following is a sample output from executing the DoubleBarrier() function call


0.0372797991359985

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