RSKBinaryBarrier




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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 bumps an input parameter given a bump map and displays the difference from the base value.

You can request to see the difference of any of the option greeks.

The name of the parameter that you wish to bump is simply entered into the 'BumpParam' string parameter.

The bump map can be a single value, a vector or a matrix input.



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


High level graphic of RSKBinaryBarrier() 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. BumpRange parameter

    A range of bump values, of which the chosen input will be bumped by. For Equity, FX type deals, you can provide a single value, vector or matrix, for interest rate type products, the bump range must be of the same shape as the market curve.
  4. BumpParam parameter

    The parameter in which will be bumped, you can only choose parameters in which the ranges normally take double (decimal) values.
  5. TypeFlag parameter

    Integer value (1 - 28) indicating option type.
  6. S parameter

    Underlying price
  7. X parameter

    Strike price of the option
  8. H parameter

    Continuous Barrier level
  9. AdjBarrFreq parameter

    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.
  10. K parameter

    Cash value to be paid.
  11. T parameter

    Time to option maturity.
  12. r 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.
  13. 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.
  14. v parameter

    Volatility of the underlying.
  15. Greek parameter

    For the option premium specify 'PREMIUM'. For all first derivatives, you can specify one of the following : 'dS' (for the 'S' parameter), 'dX' (for the 'X' parameter), 'dH' (for the 'H' parameter), 'dK' (for the 'K' parameter), 'dT' (for the 'T' parameter), 'dr' (for the 'r' parameter), 'db' (for the 'b' parameter), 'dv' (for the 'v' parameter), For second order derivatives, you can specify combinations of the first order derivatives (i.e. - 'dSdS', 'dvdv', 'dSdv'. )


Extended information

Function Syntax

VB Syntax 


Variant CTBumpRisk.RSKBinaryBarrier( _
Long ValueDate, _
DayCountEnum dayCounter, _
Variant BumpRange, _
String BumpParam, _
Variant TypeFlag, _
Variant S, _
Variant X, _
Variant H, _
Variant AdjBarrFreq, _
Variant K, _
Variant T, _
Variant r, _
Variant b, _
Variant v, _
String Greek)


Excel Spreadsheet Syntax 


=CT.RSKBinaryBarrier(
Excel Numeric Cell ValueDate,
Excel String Cell dayCounter,
XLRange BumpRange,
Excel String Cell BumpParam,
XLRange TypeFlag,
XLRange S,
XLRange X,
XLRange H,
XLRange AdjBarrFreq,
XLRange K,
XLRange T,
XLRange r,
XLRange b,
XLRange v,
Excel String Cell Greek)


C++ Syntax 


static CTRangeDataCPP RSKBinaryBarrier(
long ValueDate,
DayCountEnum dayCounter,
CTRangeDataCPP BumpRange,
std::string BumpParam,
CTRangeDataCPP TypeFlag,
CTRangeDataCPP S,
CTRangeDataCPP X,
CTRangeDataCPP H,
CTRangeDataCPP AdjBarrFreq,
CTRangeDataCPP K,
CTRangeDataCPP T,
CTRangeDataCPP r,
CTRangeDataCPP b,
CTRangeDataCPP v,
std::string Greek);


DotNET Syntax 


CTRangeData CTBumpRiskSA.RSKBinaryBarrier(
System.Int32 ValueDate,
CTIEnums.DayCountEnum dayCounter,
CTRangeData BumpRange,
System.String BumpParam,
CTRangeData TypeFlag,
CTRangeData S,
CTRangeData X,
CTRangeData H,
CTRangeData AdjBarrFreq,
CTRangeData K,
CTRangeData T,
CTRangeData r,
CTRangeData b,
CTRangeData v,
System.String Greek);

Parameter data types

ArgNameArgTypeIsKey
ValueDateLongFALSE
dayCounterDayCountEnumFALSE
BumpRangeRangeFALSE
BumpParamStringFALSE
TypeFlagRangeFALSE
SRangeFALSE
XRangeFALSE
HRangeFALSE
AdjBarrFreqRangeFALSE
KRangeFALSE
TRangeFALSE
rRangeFALSE
bRangeFALSE
vRangeFALSE
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
BumpRangeFALSERSKBinaryBarrier_BumpRange_Range (creates a range object)
BumpParamFALSEv
TypeFlagFALSERSKBinaryBarrier_TypeFlag_Range (creates a range object)
SFALSERSKBinaryBarrier_S_Range (creates a range object)
XFALSERSKBinaryBarrier_X_Range (creates a range object)
HFALSERSKBinaryBarrier_H_Range (creates a range object)
AdjBarrFreqFALSERSKBinaryBarrier_AdjBarrFreq_Range (creates a range object)
KFALSERSKBinaryBarrier_K_Range (creates a range object)
TFALSERSKBinaryBarrier_T_Range (creates a range object)
rFALSERSKBinaryBarrier_r_Range (creates a range object)
bFALSERSKBinaryBarrier_b_Range (creates a range object)
vFALSERSKBinaryBarrier_v_Range (creates a range object)
GreekFALSEPREMIUM


Example range for parameter : BumpRange

Within Excel, a range such as this can be passed directly into the BumpRange parameter.


Data is stored within the second column (Vector of data)..

Example C# API usage for setting the range data for parameter : BumpRange 


CTQL.CTRangeData RSKBinaryBarrier_BumpRange;


double[] arrBRSKBinaryBarrier_BumpRange = {
0.0192,
0.0188,
0.0193,
0.0196,
0.0183,
0.0209,
0.0197,
0.0196,
0.0194,
0.019,
0.0183,
0.0181,
0.0181,
0.0215,
0.0204,
0.0204,
0.0185,
0.0191,
0.0198,
0.02  //  Array Data

};

CTQL.DoubleVector arrRSKBinaryBarrier_BumpRange =
new  CTQL.DoubleVector(arrBRSKBinaryBarrier_BumpRange);

// Second parameter determines whether the array is a column array (false) or a row array (true)
RSKBinaryBarrier_BumpRange = new  CTQL.CTRangeData(arrRSKBinaryBarrier_BumpRange, false);

Example range for parameter : TypeFlag

Within Excel, a range such as this can be passed directly into the TypeFlag parameter.


Data is stored within the second column (Vector of data)..

Example C# API usage for setting the range data for parameter : TypeFlag 


CTQL.CTRangeData RSKBinaryBarrier_TypeFlag;


int[] arrBRSKBinaryBarrier_TypeFlag = {
11,
11,
10,
12,
10,
11,
11,
11,
11,
11,
12,
10,
10,
11,
12,
10,
11,
10,
11,
11  //  Array Data

};

CTQL.IntVector arrRSKBinaryBarrier_TypeFlag =
new  CTQL.IntVector(arrBRSKBinaryBarrier_TypeFlag);

// Second parameter determines whether the array is a column array (false) or a row array (true)
RSKBinaryBarrier_TypeFlag = new  CTQL.CTRangeData(arrRSKBinaryBarrier_TypeFlag, false);

Example range for parameter : S

Within Excel, a range such as this can be passed directly into the S parameter.


Data is stored within the second column (Vector of data)..

Example C# API usage for setting the range data for parameter : S 


CTQL.CTRangeData RSKBinaryBarrier_S;


double[] arrBRSKBinaryBarrier_S = {
114.037,
96.011,
101.3304,
114.8357,
105.3672,
102.3175,
104.7697,
105.6918,
113.5268,
98.9055,
99.0556,
112.934,
105.7505,
106.6329,
106.9273,
106.4069,
100.3174,
98.2256,
106.5198,
105.0  //  Array Data

};

CTQL.DoubleVector arrRSKBinaryBarrier_S =
new  CTQL.DoubleVector(arrBRSKBinaryBarrier_S);

// Second parameter determines whether the array is a column array (false) or a row array (true)
RSKBinaryBarrier_S = new  CTQL.CTRangeData(arrRSKBinaryBarrier_S, false);

Example range for parameter : X

Within Excel, a range such as this can be passed directly into the X parameter.


Data is stored within the second column (Vector of data)..

Example C# API usage for setting the range data for parameter : X 


CTQL.CTRangeData RSKBinaryBarrier_X;


int[] arrBRSKBinaryBarrier_X = {
96,
95,
97,
99,
96,
110,
110,
93,
108,
102,
100,
106,
101,
108,
104,
111,
94,
111,
101,
102  //  Array Data

};

CTQL.IntVector arrRSKBinaryBarrier_X =
new  CTQL.IntVector(arrBRSKBinaryBarrier_X);

// Second parameter determines whether the array is a column array (false) or a row array (true)
RSKBinaryBarrier_X = new  CTQL.CTRangeData(arrRSKBinaryBarrier_X, false);

Example range for parameter : H

Within Excel, a range such as this can be passed directly into the H parameter.


Data is stored within the second column (Vector of data)..

Example C# API usage for setting the range data for parameter : H 


CTQL.CTRangeData RSKBinaryBarrier_H;


int[] arrBRSKBinaryBarrier_H = {
103,
96,
100,
94,
96,
106,
99,
93,
99,
104,
96,
94,
99,
98,
98,
109,
102,
108,
91,
100  //  Array Data

};

CTQL.IntVector arrRSKBinaryBarrier_H =
new  CTQL.IntVector(arrBRSKBinaryBarrier_H);

// Second parameter determines whether the array is a column array (false) or a row array (true)
RSKBinaryBarrier_H = new  CTQL.CTRangeData(arrRSKBinaryBarrier_H, false);

Example range for parameter : AdjBarrFreq

Within Excel, a range such as this can be passed directly into the AdjBarrFreq parameter.


Data is stored within the second column (Vector of data)..

Example C# API usage for setting the range data for parameter : AdjBarrFreq 


CTQL.CTRangeData RSKBinaryBarrier_AdjBarrFreq;


string[] arrBRSKBinaryBarrier_AdjBarrFreq = {
"Daily",
"Daily",
"Daily",
"Daily",
"Daily",
"Daily",
"Daily",
"Daily",
"Daily",
"Daily",
"Daily",
"Daily",
"Daily",
"Daily",
"Daily",
"Daily",
"Daily",
"Daily",
"Daily",
"Daily"  //  Array Data

};

CTQL.StringVector arrRSKBinaryBarrier_AdjBarrFreq =
new  CTQL.StringVector(arrBRSKBinaryBarrier_AdjBarrFreq);

// Second parameter determines whether the array is a column array (false) or a row array (true)
RSKBinaryBarrier_AdjBarrFreq = new  CTQL.CTRangeData(arrRSKBinaryBarrier_AdjBarrFreq, false);

Example range for parameter : K

Within Excel, a range such as this can be passed directly into the K parameter.


Data is stored within the second column (Vector of data)..

Example C# API usage for setting the range data for parameter : K 


CTQL.CTRangeData RSKBinaryBarrier_K;


int[] arrBRSKBinaryBarrier_K = {
14,
14,
14,
14,
14,
16,
15,
15,
16,
16,
15,
14,
16,
14,
15,
16,
14,
16,
14,
15  //  Array Data

};

CTQL.IntVector arrRSKBinaryBarrier_K =
new  CTQL.IntVector(arrBRSKBinaryBarrier_K);

// Second parameter determines whether the array is a column array (false) or a row array (true)
RSKBinaryBarrier_K = new  CTQL.CTRangeData(arrRSKBinaryBarrier_K, false);

Example range for parameter : T

Within Excel, a range such as this can be passed directly into the T parameter.


Data is stored within the second column (Vector of data)..

Example C# API usage for setting the range data for parameter : T 


CTQL.CTRangeData RSKBinaryBarrier_T;


int[] arrBRSKBinaryBarrier_T = {
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy"),
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy"),
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy"),
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy"),
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy"),
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy"),
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy"),
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy"),
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy"),
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy"),
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy"),
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy"),
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy"),
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy"),
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy"),
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy"),
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy"),
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy"),
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy"),
CTQL.Date.serialNumber("17/1/2006", "dd/mm/yyyy")  //  Array Data

};

CTQL.IntVector arrRSKBinaryBarrier_T =
new  CTQL.IntVector(arrBRSKBinaryBarrier_T);

// Second parameter determines whether the array is a column array (false) or a row array (true)
RSKBinaryBarrier_T = new  CTQL.CTRangeData(arrRSKBinaryBarrier_T, false);

Example range for parameter : r

Within Excel, a range such as this can be passed directly into the r parameter.


Data is stored within the second column (Vector of data)..

Example C# API usage for setting the range data for parameter : r 


CTQL.CTRangeData RSKBinaryBarrier_r;


double[] arrBRSKBinaryBarrier_r = {
0.0986,
0.1001,
0.1094,
0.1089,
0.1023,
0.1052,
0.0907,
0.1003,
0.1068,
0.1004,
0.1039,
0.1095,
0.0982,
0.0937,
0.1064,
0.1001,
0.0973,
0.1092,
0.1068,
0.10  //  Array Data

};

CTQL.DoubleVector arrRSKBinaryBarrier_r =
new  CTQL.DoubleVector(arrBRSKBinaryBarrier_r);

// Second parameter determines whether the array is a column array (false) or a row array (true)
RSKBinaryBarrier_r = new  CTQL.CTRangeData(arrRSKBinaryBarrier_r, false);

Example range for parameter : b

Within Excel, a range such as this can be passed directly into the b parameter.


Data is stored within the second column (Vector of data)..

Example C# API usage for setting the range data for parameter : b 


CTQL.CTRangeData RSKBinaryBarrier_b = new CTQL.CTRangeData();

System.Text.StringBuilder RSKBinaryBarrier_b_builder =
new System.Text.StringBuilder(100);

RSKBinaryBarrier_b_builder.Append("{");
RSKBinaryBarrier_b_builder.Append("0 ;");
RSKBinaryBarrier_b_builder.Append("0 ;");
RSKBinaryBarrier_b_builder.Append("0 ;");
RSKBinaryBarrier_b_builder.Append("0 ;");
RSKBinaryBarrier_b_builder.Append("0 ;");
RSKBinaryBarrier_b_builder.Append("0 ;");
RSKBinaryBarrier_b_builder.Append("0 ;");
RSKBinaryBarrier_b_builder.Append("0 ;");
RSKBinaryBarrier_b_builder.Append("0 ;");
RSKBinaryBarrier_b_builder.Append("0 ;");
RSKBinaryBarrier_b_builder.Append("0 ;");
RSKBinaryBarrier_b_builder.Append("0 ;");
RSKBinaryBarrier_b_builder.Append("0 ;");
RSKBinaryBarrier_b_builder.Append("0 ;");
RSKBinaryBarrier_b_builder.Append("0 ;");
RSKBinaryBarrier_b_builder.Append("0 ;");
RSKBinaryBarrier_b_builder.Append("0 ;");
RSKBinaryBarrier_b_builder.Append("0 ;");
RSKBinaryBarrier_b_builder.Append("0 ;");
RSKBinaryBarrier_b_builder.Append("0.00");
RSKBinaryBarrier_b_builder.Append("}");

// Parse the string into the Range object.
RSKBinaryBarrier_b.RangeFromStr( RSKBinaryBarrier_b_builder.ToString() );

Example range for parameter : v

Within Excel, a range such as this can be passed directly into the v parameter.


Data is stored within the second column (Vector of data)..

Example C# API usage for setting the range data for parameter : v 


CTQL.CTRangeData RSKBinaryBarrier_v;


double[] arrBRSKBinaryBarrier_v = {
0.1834,
0.1854,
0.1864,
0.1999,
0.1979,
0.1866,
0.2198,
0.1997,
0.1889,
0.212,
0.1987,
0.1878,
0.2197,
0.1843,
0.2174,
0.2143,
0.1823,
0.1801,
0.1891,
0.20  //  Array Data

};

CTQL.DoubleVector arrRSKBinaryBarrier_v =
new  CTQL.DoubleVector(arrBRSKBinaryBarrier_v);

// Second parameter determines whether the array is a column array (false) or a row array (true)
RSKBinaryBarrier_v = new  CTQL.CTRangeData(arrRSKBinaryBarrier_v, false);


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 RSKBinaryBarrier() 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 RSKBinaryBarrier() function call


Example
-4.47565
3.76626
-0.126345
-3.83112
-3.39265
-0.920111
-1.74081
-3.60298
2.32433
-0.159865
-0.21598
-4.27277
0.0102712
-1.56326
-0.139104
-0.00992808
-6.10278
-0.951398
-0.569702
-3.70577



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