SOLVEQuanto




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A fixed exchange-rate foreign-equity option (Quanto) is denominated in another currency than that of the underlying equity exposure.

The face value of the currency protection expands or contracts to cover changes in the foreign currency value of the underlying asset.

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.



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


High level graphic of SOLVEQuanto() function with parameters. Blue square node is the actual function with the parameters ordered.



Parameter Description


  1. ValueDate parameter

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

    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.
  3. PremiumVal parameter

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

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

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

    This parameter cannot be solved for. Option Types (C)all or (P)ut
  7. Ep parameter

    Predetermined exchange rate specified in units of domestic currency per unit of foreign currency.
  8. S parameter

    Underlying price in foreign currency
  9. X parameter

    Delivery price in foreign currency
  10. T parameter

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

    Domestic interest rate
  12. rf parameter

    Foreign interest rate.
  13. q parameter

    Instantaneous proportional dividend payout rate of the underlying asset
  14. vS parameter

    Volatility of the underlying asset.
  15. vE parameter

    Volatility of the domestic exchange rate.
  16. rho parameter

    Correlation between the asset and the domestic exchange rate.
  17. SolveFor parameter

    The parameter in which you would like to solve for.


Extended information

Function Syntax

VB Syntax 


Double CTOptionSolver.SOLVEQuanto( _
Long ValueDate, _
DayCountEnum dayCounter, _
Double PremiumVal, _
String SolverKey, _
Double tolerance, _
String CallPut, _
Double Ep, _
Double S, _
Double X, _
Long T, _
Double r, _
Double rf, _
Double q, _
Double vS, _
Double vE, _
Double rho, _
String SolveFor)


Excel Spreadsheet Syntax 


=CT.SOLVEQuanto(
Excel Numeric Cell ValueDate,
Excel String Cell dayCounter,
Excel Numeric Cell PremiumVal,
Excel String Cell SolverKey,
Excel Numeric Cell tolerance,
Excel String Cell CallPut,
Excel Numeric Cell Ep,
Excel Numeric Cell S,
Excel Numeric Cell X,
Excel Numeric Cell T,
Excel Numeric Cell r,
Excel Numeric Cell rf,
Excel Numeric Cell q,
Excel Numeric Cell vS,
Excel Numeric Cell vE,
Excel Numeric Cell rho,
Excel String Cell SolveFor)


C++ Syntax 


static double SOLVEQuanto(
long ValueDate,
DayCountEnum dayCounter,
double PremiumVal,
std::string SolverKey,
double tolerance,
std::string CallPut,
double Ep,
double S,
double X,
long T,
double r,
double rf,
double q,
double vS,
double vE,
double rho,
std::string SolveFor);


DotNET Syntax 


System.Double CTOptionSolverSA.SOLVEQuanto(
System.Int32 ValueDate,
CTIEnums.DayCountEnum dayCounter,
System.Double PremiumVal,
System.String SolverKey,
System.Double tolerance,
System.String CallPut,
System.Double Ep,
System.Double S,
System.Double X,
System.Int32 T,
System.Double r,
System.Double rf,
System.Double q,
System.Double vS,
System.Double vE,
System.Double rho,
System.String SolveFor);

Parameter data types

ArgNameArgTypeIsKey
ValueDateLongFALSE
dayCounterDayCountEnumFALSE
PremiumValDoubleFALSE
SolverKeyStringTRUE
toleranceDoubleFALSE
CallPutStringFALSE
EpDoubleFALSE
SDoubleFALSE
XDoubleFALSE
TLongFALSE
rDoubleFALSE
rfDoubleFALSE
qDoubleFALSE
vSDoubleFALSE
vEDoubleFALSE
rhoDoubleFALSE
SolveForStringFALSE

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
PremiumValFALSE0.5
SolverKeyFALSESolverKeyNAME.EXTTAG.TICKER (from a function call)
toleranceFALSE0.0001
CallPutFALSECall
EpFALSE1.5
SFALSE100.0
XFALSE105
TFALSE17/Jan/2006 (serial date type)
rFALSE0.08
rfFALSE0.05
qFALSE0.04
vSFALSE0.20
vEFALSE0.10
rhoFALSE0.3
SolveForFALSEvS


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 SOLVEQuanto() 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.

These are the financial QuantTools sub-function calls that are used within the examples :





The objects generated by these sub-functions are inter-connected in the following way :




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 SOLVEQuanto() function call


0.0612609512853099

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