Look-barrier options can be regarded as a combination of a partial time barrier option and a forward starting fixed strike lookback option.

The look-barrier option's barrier monitoring period starts at the option's starting date and ends at an arbitrary date t1 before expiration.

If the barrier is not hit during the monitoring period, the fixed strike lookback option will be initiated at the same time the barrier ceases to exist.

By introducing a knock-out barrier in the first part of the option's lifetime, the option will be cheaper than a standard partial-time fixed strike lookback option.

Values for the TypeFlag parameter are - cuo (Up-and-out call (H greater than S)), cui (Up-and-in call (H greater than S)), pdo (Down-and-out put (H less than S)) and pdi (Down-and-in put (H less than S)).

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).

This function returns a partial derivative matrix of all second order derivatives (Hessian matrix).

Each individual second order derivative as well as the first order derivatives can be obtained, individually, via the pricing functions present within the CapeTools Exotic Options category of functions.

However this function computes all the second order risk numbers in a single function call.

Variant CTDerivativeMatrix.DM_LookBarrier( _
Long ValueDate, _
DayCountEnum dayCounter, _
String TypeFlag, _
Double S, _
Double X, _
Double H, _
String AdjBarrFreq, _
Long t1, _
Long T2, _
Double r, _
Double b, _
Double v)

=CT.DM_LookBarrier(
Excel Numeric Cell ValueDate,
Excel String Cell dayCounter,
Excel String Cell TypeFlag,
Excel Numeric Cell S,
Excel Numeric Cell X,
Excel Numeric Cell H,
Excel String Cell AdjBarrFreq,
Excel Numeric Cell t1,
Excel Numeric Cell T2,
Excel Numeric Cell r,
Excel Numeric Cell b,
Excel Numeric Cell v)

static CTRangeDataCPP DM_LookBarrier(
long ValueDate,
DayCountEnum dayCounter,
std::string TypeFlag,
double S,
double X,
double H,
std::string AdjBarrFreq,
long t1,
long T2,
double r,
double b,
double v);

CTRangeData CTDerivativeMatrixSA.DM_LookBarrier(
System.Int32 ValueDate,
CTIEnums.DayCountEnum dayCounter,
System.String TypeFlag,
System.Double S,
System.Double X,
System.Double H,
System.String AdjBarrFreq,
System.Int32 t1,
System.Int32 T2,
System.Double r,
System.Double b,
System.Double v);

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.