SOLVEBinaryBarrier

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 tries to solve for the value indicated by the 'SolveFor' parameter.

Simply enter the name of the parameter you wish to solve for.

This parameter cannot be solved for. Valuation Date (typically equal to Today's date)

This parameter cannot be solved for. 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.

This parameter cannot be solved for. Premium Value that will be tested against.

This parameter cannot be solved for. Key to an already created Solver object (Within the 'CapeTools One-Dimensional Solvers' category of functions).

This parameter cannot be solved for. tolerance (ie - 0.0001).

This parameter cannot be solved for. Integer value (1 - 28) indicating option type.

Strike price of the option

Continuous Barrier level

This parameter cannot be solved for. Monitoring frequency that you wish the continuous 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.

Cash value to be paid.

This parameter cannot be solved for. Time to option maturity.

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.

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.

Volatility of the underlying.

The parameter in which you would like to solve for.


Double CTOptionSolver.SOLVEBinaryBarrier( _
Long ValueDate, _
DayCountEnum dayCounter, _
Double PremiumVal, _
String SolverKey, _
Double tolerance, _
Long TypeFlag, _
Double S, _
Double X, _
Double H, _
String AdjBarrFreq, _
Double K, _
Long T, _
Double r, _
Double b, _
Double v, _
String SolveFor)


=CT.SOLVEBinaryBarrier(
Excel Numeric Cell ValueDate,
Excel String Cell dayCounter,
Excel Numeric Cell PremiumVal,
Excel String Cell SolverKey,
Excel Numeric Cell tolerance,
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,
Excel String Cell SolveFor)


static double SOLVEBinaryBarrier(
long ValueDate,
DayCountEnum dayCounter,
double PremiumVal,
std::string SolverKey,
double tolerance,
long TypeFlag,
double S,
double X,
double H,
std::string AdjBarrFreq,
double K,
long T,
double r,
double b,
double v,
std::string SolveFor);


System.Double CTOptionSolverSA.SOLVEBinaryBarrier(
System.Int32 ValueDate,
CTIEnums.DayCountEnum dayCounter,
System.Double PremiumVal,
System.String SolverKey,
System.Double tolerance,
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,
System.String SolveFor);

ArgName	ArgType	IsKey
ValueDate	Long	FALSE
dayCounter	DayCountEnum	FALSE
PremiumVal	Double	FALSE
SolverKey	String	TRUE
tolerance	Double	FALSE
TypeFlag	Long	FALSE
S	Double	FALSE
X	Double	FALSE
H	Double	FALSE
AdjBarrFreq	String	FALSE
K	Double	FALSE
T	Long	FALSE
r	Double	FALSE
b	Double	FALSE
v	Double	FALSE
SolveFor	String	FALSE

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.

ArgName	IsOptional (Excel only)	Example
ValueDate	FALSE	19/Jul/2005 (serial date type)
dayCounter	FALSE	ACT365
PremiumVal	FALSE	42
SolverKey	FALSE	SolverKeyNAME.EXTTAG.TICKER (from a function call)
tolerance	FALSE	0.0001
TypeFlag	FALSE	11
S	FALSE	105.0
X	FALSE	102
H	FALSE	100
AdjBarrFreq	FALSE	Daily
K	FALSE	15
T	FALSE	17/Jan/2006 (serial date type)
r	FALSE	0.10
b	FALSE	0.00
v	FALSE	0.20
SolveFor	FALSE	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.