There are 28 different types of so-called binary options.

The binary barrier options can be divided into two categories.

Cash-or-nothing barrier options.

These either pay out a pre-specified cash amount or nothing, depending on whether the asset price has hit the barrier or not.

The other category is the asset-or-nothing barrier options, which pay out the value of the asset or nothing, depending on whether the asset price has hit the barrier or not.

The 28 different types of options are : TypeFlag=1 implying Down-and-in cash-(at-hit)-or-nothing (S greater than H).

TypeFlag=2 implying Up-and-in cash-(at-hit)-or-nothing (S less than H).

TypeFlag=3 implying Down-and-in asset-(at-hit)-or-nothing (K=H) (S greater than H).

TypeFlag=4 implying Up-and-in asset-(at-hit)-or-nothing (K=H)(S less than H).

TypeFlag=5 implying Down-and-in cash-(at-expiry)-or-nothing (S greater than H).

TypeFlag=6 implying Up-and-in cash-(at-expiry)-or-nothing (S less than H).

TypeFlag=7 implying Down-and-in asset-(at-expiry)-or-nothing (S greater than H).

TypeFlag=8 implying Up-and-in asset-(at-expiry)-or-nothing (S less than H).

TypeFlag=9 implying Down-and-out cash-(at-expiry)-or-nothing (S greater than H).

TypeFlag=10 implying Up-and-out cash-(at-expiry)-or-nothing (S less than H).

TypeFlag=11 implying Down-and-out asset-(at-expiry)-or-nothing (S greater than H).

TypeFlag=12 implying Up-and-out asset-(at-expiry)-or-nothing (S less than H).

TypeFlag=13 implying Down-and-in cash-(at-expiry)-or-nothing call (S greater than H).

TypeFlag=14 implying Up-and-in cash-(at-expiry)-or-nothing call (S less than H).

TypeFlag=15 implying Down-and-in asset-(at-expiry)-or-nothing call (S greater than H).

TypeFlag=16 implying Up-and-in asset-(at-expiry)-or-nothing call (S less than H).

TypeFlag=17 implying Down-and-in cash-(at-expiry)-or-nothing put (S greater than H).

TypeFlag=18 implying Up-and-in cash-(at-expiry)-or-nothing put (S less than H).

TypeFlag=19 implying Down-and-in asset-(at-expiry)-or-nothing put (S greater than H).

TypeFlag=20 implying Up-and-in asset-(at-expiry)-or-nothing put (S less than H).

TypeFlag=21 implying Down-and-out cash-(at-expiry)-or-nothing call (S greater than H).

TypeFlag=22 implying Up-and-out cash-(at-expiry)-or-nothing call (S less than H).

TypeFlag=23 implying Down-and-out asset-(at-expiry)-or-nothing call (S greater than H).

TypeFlag=24 implying Up-and-out asset-(at-expiry)-or-nothing call (S less than H).

TypeFlag=25 implying Down-and-out cash-(at-expiry)-or-nothing put (S greater than H).

TypeFlag=26 implying Up-and-out cash-(at-expiry)-or-nothing put (S less than H).

TypeFlag=27 implying Down-and-out asset-(at-expiry)-or-nothing put (S greater than H).

TypeFlag=28 implying Up-and-out asset-(at-expiry)-or-nothing put (S less than H).

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_BinaryBarrier( _
Long ValueDate, _
DayCountEnum dayCounter, _
Long TypeFlag, _
Double S, _
Double X, _
Double H, _
String AdjBarrFreq, _
Double K, _
Long T, _
Double r, _
Double b, _
Double v)

=CT.DM_BinaryBarrier(
Excel Numeric Cell ValueDate,
Excel String Cell dayCounter,
Excel Numeric Cell TypeFlag,
Excel Numeric Cell S,
Excel Numeric Cell X,
Excel Numeric Cell H,
Excel String Cell AdjBarrFreq,
Excel Numeric Cell K,
Excel Numeric Cell T,
Excel Numeric Cell r,
Excel Numeric Cell b,
Excel Numeric Cell v)

static CTRangeDataCPP DM_BinaryBarrier(
long ValueDate,
DayCountEnum dayCounter,
long TypeFlag,
double S,
double X,
double H,
std::string AdjBarrFreq,
double K,
long T,
double r,
double b,
double v);

CTRangeData CTDerivativeMatrixSA.DM_BinaryBarrier(
System.Int32 ValueDate,
CTIEnums.DayCountEnum dayCounter,
System.Int32 TypeFlag,
System.Double S,
System.Double X,
System.Double H,
System.String AdjBarrFreq,
System.Double K,
System.Int32 T,
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.