Call option, the strike is fixed in advance and at expiry the option pays out the max of the difference between the highest observed price Smax and the strike X and 0. A put at expiry pays out the max of the difference between the fixed strike X and the min observed price Smin and 0. The lookback period starts after t1 which is after the initialization date of the option.

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_PartialFixedLB( _
Long ValueDate, _
DayCountEnum dayCounter, _
String CallPut, _
Double Underlying, _
Double X, _
Long Timet1, _
Long TimeT2, _
Double Rate, _
Double B, _
Double Vol)

=CT.DM_PartialFixedLB(
Excel Numeric Cell ValueDate,
Excel String Cell dayCounter,
Excel String Cell CallPut,
Excel Numeric Cell Underlying,
Excel Numeric Cell X,
Excel Numeric Cell Timet1,
Excel Numeric Cell TimeT2,
Excel Numeric Cell Rate,
Excel Numeric Cell B,
Excel Numeric Cell Vol)

static CTRangeDataCPP DM_PartialFixedLB(
long ValueDate,
DayCountEnum dayCounter,
std::string CallPut,
double Underlying,
double X,
long Timet1,
long TimeT2,
double Rate,
double B,
double Vol);

CTRangeData CTDerivativeMatrixSA.DM_PartialFixedLB(
System.Int32 ValueDate,
CTIEnums.DayCountEnum dayCounter,
System.String CallPut,
System.Double Underlying,
System.Double X,
System.Int32 Timet1,
System.Int32 TimeT2,
System.Double Rate,
System.Double B,
System.Double Vol);

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.