MEuropeanExchangeOption




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Option to exchange one asset for another at expiration.

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 prices a portfolio of equity, commodities, futures or FX option deals from raw inputs.

All memory is discarded once the computation is finished.

You can request for all first and second order risk statistics simply by filling in the greek field with the name of the parameter.

The name of the parameter must be proceeded with the character 'd'. Thus if 'Stock', 'Time' and 'Vol' are the names of three parameters which represent underlying price, Option Maturity and option volatility respectively, you can request DELTA as 'dStock', GAMMA as 'dStockdStock' (dStock twice), VEGA as 'dVol', THETA as 'dTime', VOLGA as 'dVoldVol' (dVol twice) and VANNA (cross-derivative) as 'dStockdVol' or 'dVoldStock'. You can also, if you wish request 'dTimedVol' (second derivative with respect to Time and Vol).

If you wish to view all the second order derivatives within a matrix, please refer to the CapeTools Derivative Matrix category of functions.

This logic can be applied to any parameter which is of a double-valued type (decimal value).

The risk statistics are the partial derivatives with respect to the option price, thus you can scale the results by multiplying by a factor.

For example, to compute the VEGA for a one percent change in volatility (0.01), simply multiply the VEGA result by 0.01. To compute THETA for a one day change (1/365), multiply the THETA result by 1/365. To compute the DELTA for a one-unit change (1), multiply the delta by 1 which is, of course the same result as the original delta.

For second order risks, simply multiply by the product of the changes.



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


High level graphic of MEuropeanExchangeOption() 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. Units parameter

    Number of option contracts you wish to trade in (positive value).
  4. Position parameter

    Whether you are long or short the option.
  5. Level parameter

    Whether you would like to view the PV for the entire structure/portfolio 'TOTAL'. Whether you would like to view the PV for each option 'CASHFLOW'. Or whether you would like to view the PV and extended information, 'ALL'. Thus valid values are - 'TOTAL', 'CASHFLOW' or 'ALL'.
  6. Underlying1 parameter

    Price of the first underlying
  7. Underlying2 parameter

    Price of the second underlying
  8. Quantity1 parameter

    Quantity of the first underlying.
  9. Quantity2 parameter

    Quantity of the second underlying.
  10. Time parameter

    Expiration date of the option.
  11. Rate 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.
  12. b1 parameter

    For the first 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.
  13. b2 parameter

    For the second 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. Vol1 parameter

    Volatility of the underlying Price1.
  15. Vol2 parameter

    Volatility of the underlying Price2.
  16. Rho parameter

    Correlation between the two assets.
  17. Greek parameter

    For the option premium specify 'PREMIUM'. For all first derivatives, you can specify one of the following : 'dUnderlying1' (for the 'Underlying1' parameter), 'dUnderlying2' (for the 'Underlying2' parameter), 'dQuantity1' (for the 'Quantity1' parameter), 'dQuantity2' (for the 'Quantity2' parameter), 'dTime' (for the 'Time' parameter), 'dRate' (for the 'Rate' parameter), 'db1' (for the 'b1' parameter), 'db2' (for the 'b2' parameter), 'dVol1' (for the 'Vol1' parameter), 'dVol2' (for the 'Vol2' parameter), 'dRho' (for the 'Rho' parameter), For second order derivatives, you can specify combinations of the first order derivatives (i.e. - 'dUnderlying1dUnderlying1', 'dVol1dVol1', 'dUnderlying1dVol1'. )


Extended information

Function Syntax

VB Syntax 


Variant CTExoticAnalysis.MEuropeanExchangeOption( _
Long ValueDate, _
DayCountEnum dayCounter, _
Variant Units, _
Variant Position, _
String Level, _
Variant Underlying1, _
Variant Underlying2, _
Variant Quantity1, _
Variant Quantity2, _
Variant Time, _
Variant Rate, _
Variant b1, _
Variant b2, _
Variant Vol1, _
Variant Vol2, _
Variant Rho, _
String Greek)


Excel Spreadsheet Syntax 


=CT.MEuropeanExchangeOption(
Excel Numeric Cell ValueDate,
Excel String Cell dayCounter,
XLRange Units,
XLRange Position,
Excel String Cell Level,
XLRange Underlying1,
XLRange Underlying2,
XLRange Quantity1,
XLRange Quantity2,
XLRange Time,
XLRange Rate,
XLRange b1,
XLRange b2,
XLRange Vol1,
XLRange Vol2,
XLRange Rho,
Excel String Cell Greek)


C++ Syntax 


static CTRangeDataCPP MEuropeanExchangeOption(
long ValueDate,
DayCountEnum dayCounter,
CTRangeDataCPP Units,
CTRangeDataCPP Position,
std::string Level,
CTRangeDataCPP Underlying1,
CTRangeDataCPP Underlying2,
CTRangeDataCPP Quantity1,
CTRangeDataCPP Quantity2,
CTRangeDataCPP Time,
CTRangeDataCPP Rate,
CTRangeDataCPP b1,
CTRangeDataCPP b2,
CTRangeDataCPP Vol1,
CTRangeDataCPP Vol2,
CTRangeDataCPP Rho,
std::string Greek);


DotNET Syntax 


CTRangeData CTExoticAnalysisSA.MEuropeanExchangeOption(
System.Int32 ValueDate,
CTIEnums.DayCountEnum dayCounter,
CTRangeData Units,
CTRangeData Position,
System.String Level,
CTRangeData Underlying1,
CTRangeData Underlying2,
CTRangeData Quantity1,
CTRangeData Quantity2,
CTRangeData Time,
CTRangeData Rate,
CTRangeData b1,
CTRangeData b2,
CTRangeData Vol1,
CTRangeData Vol2,
CTRangeData Rho,
System.String Greek);

Parameter data types

ArgNameArgTypeIsKey
ValueDateLongFALSE
dayCounterDayCountEnumFALSE
UnitsRangeFALSE
PositionRangeFALSE
LevelStringFALSE
Underlying1RangeFALSE
Underlying2RangeFALSE
Quantity1RangeFALSE
Quantity2RangeFALSE
TimeRangeFALSE
RateRangeFALSE
b1RangeFALSE
b2RangeFALSE
Vol1RangeFALSE
Vol2RangeFALSE
RhoRangeFALSE
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
UnitsFALSEMEuropeanExchangeOption_Units_Range (creates a range object)
PositionFALSEMEuropeanExchangeOption_Position_Range (creates a range object)
LevelFALSEALL
Underlying1FALSEMEuropeanExchangeOption_Underlying1_Range (creates a range object)
Underlying2FALSEMEuropeanExchangeOption_Underlying2_Range (creates a range object)
Quantity1FALSEMEuropeanExchangeOption_Quantity1_Range (creates a range object)
Quantity2FALSEMEuropeanExchangeOption_Quantity2_Range (creates a range object)
TimeFALSEMEuropeanExchangeOption_Time_Range (creates a range object)
RateFALSEMEuropeanExchangeOption_Rate_Range (creates a range object)
b1FALSEMEuropeanExchangeOption_b1_Range (creates a range object)
b2FALSEMEuropeanExchangeOption_b2_Range (creates a range object)
Vol1FALSEMEuropeanExchangeOption_Vol1_Range (creates a range object)
Vol2FALSEMEuropeanExchangeOption_Vol2_Range (creates a range object)
RhoFALSEMEuropeanExchangeOption_Rho_Range (creates a range object)
GreekFALSEPREMIUM


Example range for parameter : Units

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


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

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


CTQL.CTRangeData MEuropeanExchangeOption_Units;


int[] arrBMEuropeanExchangeOption_Units = {
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1  //  Array Data

};

CTQL.IntVector arrMEuropeanExchangeOption_Units =
new  CTQL.IntVector(arrBMEuropeanExchangeOption_Units);

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

Example range for parameter : Position

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


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

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


CTQL.CTRangeData MEuropeanExchangeOption_Position;


string[] arrBMEuropeanExchangeOption_Position = {
"LONG",
"LONG",
"LONG",
"LONG",
"LONG",
"LONG",
"LONG",
"LONG",
"LONG",
"LONG",
"LONG",
"LONG",
"LONG",
"LONG",
"LONG",
"LONG",
"LONG",
"LONG",
"LONG",
"LONG"  //  Array Data

};

CTQL.StringVector arrMEuropeanExchangeOption_Position =
new  CTQL.StringVector(arrBMEuropeanExchangeOption_Position);

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

Example range for parameter : Underlying1

Within Excel, a range such as this can be passed directly into the Underlying1 parameter.


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

Example C# API usage for setting the range data for parameter : Underlying1 


CTQL.CTRangeData MEuropeanExchangeOption_Underlying1;


int[] arrBMEuropeanExchangeOption_Underlying1 = {
111,
110,
92,
96,
91,
92,
101,
91,
106,
109,
109,
97,
110,
98,
100,
108,
106,
93,
93,
101  //  Array Data

};

CTQL.IntVector arrMEuropeanExchangeOption_Underlying1 =
new  CTQL.IntVector(arrBMEuropeanExchangeOption_Underlying1);

// Second parameter determines whether the array is a column array (false) or a row array (true)
MEuropeanExchangeOption_Underlying1 = new  CTQL.CTRangeData(arrMEuropeanExchangeOption_Underlying1, false);

Example range for parameter : Underlying2

Within Excel, a range such as this can be passed directly into the Underlying2 parameter.


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

Example C# API usage for setting the range data for parameter : Underlying2 


CTQL.CTRangeData MEuropeanExchangeOption_Underlying2;


int[] arrBMEuropeanExchangeOption_Underlying2 = {
111,
112,
101,
99,
104,
95,
103,
100,
107,
94,
109,
105,
94,
109,
96,
114,
97,
95,
98,
104  //  Array Data

};

CTQL.IntVector arrMEuropeanExchangeOption_Underlying2 =
new  CTQL.IntVector(arrBMEuropeanExchangeOption_Underlying2);

// Second parameter determines whether the array is a column array (false) or a row array (true)
MEuropeanExchangeOption_Underlying2 = new  CTQL.CTRangeData(arrMEuropeanExchangeOption_Underlying2, false);

Example range for parameter : Quantity1

Within Excel, a range such as this can be passed directly into the Quantity1 parameter.


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

Example C# API usage for setting the range data for parameter : Quantity1 


CTQL.CTRangeData MEuropeanExchangeOption_Quantity1;


int[] arrBMEuropeanExchangeOption_Quantity1 = {
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1  //  Array Data

};

CTQL.IntVector arrMEuropeanExchangeOption_Quantity1 =
new  CTQL.IntVector(arrBMEuropeanExchangeOption_Quantity1);

// Second parameter determines whether the array is a column array (false) or a row array (true)
MEuropeanExchangeOption_Quantity1 = new  CTQL.CTRangeData(arrMEuropeanExchangeOption_Quantity1, false);

Example range for parameter : Quantity2

Within Excel, a range such as this can be passed directly into the Quantity2 parameter.


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

Example C# API usage for setting the range data for parameter : Quantity2 


CTQL.CTRangeData MEuropeanExchangeOption_Quantity2;


int[] arrBMEuropeanExchangeOption_Quantity2 = {
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1  //  Array Data

};

CTQL.IntVector arrMEuropeanExchangeOption_Quantity2 =
new  CTQL.IntVector(arrBMEuropeanExchangeOption_Quantity2);

// Second parameter determines whether the array is a column array (false) or a row array (true)
MEuropeanExchangeOption_Quantity2 = new  CTQL.CTRangeData(arrMEuropeanExchangeOption_Quantity2, false);

Example range for parameter : Time

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


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

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


CTQL.CTRangeData MEuropeanExchangeOption_Time;


int[] arrBMEuropeanExchangeOption_Time = {
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 arrMEuropeanExchangeOption_Time =
new  CTQL.IntVector(arrBMEuropeanExchangeOption_Time);

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

Example range for parameter : Rate

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


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

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


CTQL.CTRangeData MEuropeanExchangeOption_Rate;


double[] arrBMEuropeanExchangeOption_Rate = {
0.091,
0.1063,
0.1095,
0.1066,
0.0932,
0.1034,
0.0921,
0.1024,
0.1006,
0.1022,
0.0976,
0.1047,
0.1022,
0.0969,
0.1001,
0.1026,
0.0972,
0.0911,
0.1047,
0.1  //  Array Data

};

CTQL.DoubleVector arrMEuropeanExchangeOption_Rate =
new  CTQL.DoubleVector(arrBMEuropeanExchangeOption_Rate);

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

Example range for parameter : b1

Within Excel, a range such as this can be passed directly into the b1 parameter.


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

Example C# API usage for setting the range data for parameter : b1 


CTQL.CTRangeData MEuropeanExchangeOption_b1;


double[] arrBMEuropeanExchangeOption_b1 = {
0.0188,
0.0193,
0.0188,
0.0185,
0.0196,
0.0196,
0.0187,
0.022,
0.0208,
0.0182,
0.0208,
0.0186,
0.0196,
0.0209,
0.0207,
0.0206,
0.0214,
0.0205,
0.0194,
0.02  //  Array Data

};

CTQL.DoubleVector arrMEuropeanExchangeOption_b1 =
new  CTQL.DoubleVector(arrBMEuropeanExchangeOption_b1);

// Second parameter determines whether the array is a column array (false) or a row array (true)
MEuropeanExchangeOption_b1 = new  CTQL.CTRangeData(arrMEuropeanExchangeOption_b1, false);

Example range for parameter : b2

Within Excel, a range such as this can be passed directly into the b2 parameter.


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

Example C# API usage for setting the range data for parameter : b2 


CTQL.CTRangeData MEuropeanExchangeOption_b2;


double[] arrBMEuropeanExchangeOption_b2 = {
0.0364,
0.0401,
0.0376,
0.0367,
0.0365,
0.043,
0.0374,
0.0381,
0.0393,
0.0394,
0.0434,
0.044,
0.0401,
0.0401,
0.0421,
0.0392,
0.0423,
0.0392,
0.038,
0.04  //  Array Data

};

CTQL.DoubleVector arrMEuropeanExchangeOption_b2 =
new  CTQL.DoubleVector(arrBMEuropeanExchangeOption_b2);

// Second parameter determines whether the array is a column array (false) or a row array (true)
MEuropeanExchangeOption_b2 = new  CTQL.CTRangeData(arrMEuropeanExchangeOption_b2, false);

Example range for parameter : Vol1

Within Excel, a range such as this can be passed directly into the Vol1 parameter.


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

Example C# API usage for setting the range data for parameter : Vol1 


CTQL.CTRangeData MEuropeanExchangeOption_Vol1;


double[] arrBMEuropeanExchangeOption_Vol1 = {
0.1635,
0.1671,
0.1811,
0.1706,
0.1862,
0.1665,
0.1692,
0.1842,
0.1848,
0.1699,
0.1709,
0.1886,
0.1881,
0.1917,
0.1631,
0.1924,
0.1724,
0.1888,
0.1871,
0.18  //  Array Data

};

CTQL.DoubleVector arrMEuropeanExchangeOption_Vol1 =
new  CTQL.DoubleVector(arrBMEuropeanExchangeOption_Vol1);

// Second parameter determines whether the array is a column array (false) or a row array (true)
MEuropeanExchangeOption_Vol1 = new  CTQL.CTRangeData(arrMEuropeanExchangeOption_Vol1, false);

Example range for parameter : Vol2

Within Excel, a range such as this can be passed directly into the Vol2 parameter.


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

Example C# API usage for setting the range data for parameter : Vol2 


CTQL.CTRangeData MEuropeanExchangeOption_Vol2;


double[] arrBMEuropeanExchangeOption_Vol2 = {
0.1209,
0.1198,
0.1144,
0.1249,
0.1094,
0.1125,
0.1239,
0.1168,
0.1273,
0.1083,
0.114,
0.1234,
0.1099,
0.1107,
0.1184,
0.13,
0.1094,
0.1087,
0.117,
0.12  //  Array Data

};

CTQL.DoubleVector arrMEuropeanExchangeOption_Vol2 =
new  CTQL.DoubleVector(arrBMEuropeanExchangeOption_Vol2);

// Second parameter determines whether the array is a column array (false) or a row array (true)
MEuropeanExchangeOption_Vol2 = new  CTQL.CTRangeData(arrMEuropeanExchangeOption_Vol2, false);

Example range for parameter : Rho

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


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

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


CTQL.CTRangeData MEuropeanExchangeOption_Rho;


double[] arrBMEuropeanExchangeOption_Rho = {
0.844,
0.8688,
0.7314,
0.7629,
0.8008,
0.7598,
0.8552,
0.7218,
0.7735,
0.8534,
0.739,
0.7762,
0.7328,
0.8077,
0.7789,
0.8279,
0.7434,
0.799,
0.7761,
0.8  //  Array Data

};

CTQL.DoubleVector arrMEuropeanExchangeOption_Rho =
new  CTQL.DoubleVector(arrBMEuropeanExchangeOption_Rho);

// Second parameter determines whether the array is a column array (false) or a row array (true)
MEuropeanExchangeOption_Rho = new  CTQL.CTRangeData(arrMEuropeanExchangeOption_Rho, 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 MEuropeanExchangeOption() 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 MEuropeanExchangeOption() function call


Example
NoOfUnitsPositionUnderlying1Underlying2Quantity1Quantity2TimeRateb1b2Vol1Vol2RhoPREMIUM
1LONG9711111387340.0960.01870.03990.19210.13130.78690.275842
1LONG939611387340.09170.01920.03950.17540.12880.781.99038
1LONG10410011387340.0980.02190.04010.16340.11870.74896.08084
1LONG9911311387340.1080.01850.03960.19490.11620.86680.208025
1LONG1089411387340.10510.02020.03860.18440.11920.829314.7866
1LONG9410711387340.09120.01890.03670.18670.12190.74330.355248
1LONG10011011387340.10430.01940.03830.17520.13050.78720.517977
1LONG9910011387340.09950.02080.03720.17610.11320.84792.67412
1LONG10510211387340.10460.02190.03920.16380.10840.79835.21471
1LONG1029411387340.09590.02150.04050.16380.12350.829.04432
1LONG10710311387340.10620.02180.03610.18260.12860.80566.06921
1LONG9410211387340.09110.02080.04260.16660.11640.7270.817444
1LONG10610011387340.1030.02190.0370.16290.11260.75857.48289
1LONG10510911387340.10620.01910.03970.19180.12360.74652.57237
1LONG10211411387340.10360.02130.03930.17590.12060.84540.227255
1LONG10011311387340.09920.02180.04080.17990.1220.86970.136293
1LONG9410411387340.1020.02130.03720.18840.10840.86390.416336
1LONG10410011387340.10350.01830.04080.18070.12780.79026.32296
1LONG10510011387340.09340.01990.04090.16610.11470.79426.82889
1LONG10110411387340.10.020.040.180.120.82.26737



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