TurnbullWakemanAsian




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CapeTools Exotic Options function list

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It is not possible to find a closed form solution for the valuation of options on an arithmetic average.

The main reason for this is that when the asset is assumed to be lognormally distributed, the arithmetic average will not itself have a lognormal distribution.

Arithmetic average-rate options can be priced by analytical approximations or by Monte-carlo simulations.

This function uses an analytical approximation devised by Turnbull and Wakeman.

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).



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


High level graphic of TurnbullWakemanAsian() 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. CallPut parameter

    Option Types (C)all or (P)ut
  4. S parameter

    Underlying price
  5. SA parameter

    Arithmetic average of the known asset price fixings.
  6. X parameter

    Strike price of the option
  7. T parameter

    Original time to option maturity.
  8. T2 parameter

    Remaining time to option maturity.
  9. tau parameter

    Time to start of average period.
  10. 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.
  11. 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.
  12. v parameter

    Volatility of the underlying.
  13. Greek parameter

    For the option premium specify 'PREMIUM'. For all first derivatives, you can specify one of the following : 'dS' (for the 'S' parameter), 'dSA' (for the 'SA' parameter), 'dX' (for the 'X' parameter), 'dT' (for the 'T' parameter), 'dT2' (for the 'T2' parameter), 'dtau' (for the 'tau' 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 


Double CTExoticOptions.TurnbullWakemanAsian( _
Long ValueDate, _
DayCountEnum dayCounter, _
String CallPut, _
Double S, _
Double SA, _
Double X, _
Long T, _
Long T2, _
Long tau, _
Double r, _
Double b, _
Double v, _
String Greek)


Excel Spreadsheet Syntax 


=CT.EXO.TurnbullWakemanAsian(
Excel Numeric Cell ValueDate,
Excel String Cell dayCounter,
Excel String Cell CallPut,
Excel Numeric Cell S,
Excel Numeric Cell SA,
Excel Numeric Cell X,
Excel Numeric Cell T,
Excel Numeric Cell T2,
Excel Numeric Cell tau,
Excel Numeric Cell r,
Excel Numeric Cell b,
Excel Numeric Cell v,
Excel String Cell Greek)


C++ Syntax 


static double TurnbullWakemanAsian(
long ValueDate,
DayCountEnum dayCounter,
std::string CallPut,
double S,
double SA,
double X,
long T,
long T2,
long tau,
double r,
double b,
double v,
std::string Greek);


DotNET Syntax 


System.Double CTExoticOptionsSA.TurnbullWakemanAsian(
System.Int32 ValueDate,
CTIEnums.DayCountEnum dayCounter,
System.String CallPut,
System.Double S,
System.Double SA,
System.Double X,
System.Int32 T,
System.Int32 T2,
System.Int32 tau,
System.Double r,
System.Double b,
System.Double v,
System.String Greek);

Parameter data types

ArgNameArgTypeIsKey
ValueDateLongFALSE
dayCounterDayCountEnumFALSE
CallPutStringFALSE
SDoubleFALSE
SADoubleFALSE
XDoubleFALSE
TLongFALSE
T2LongFALSE
tauLongFALSE
rDoubleFALSE
bDoubleFALSE
vDoubleFALSE
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
CallPutFALSECall
SFALSE100.0
SAFALSE110
XFALSE95
TFALSE19/Apr/2006 (serial date type)
T2FALSE17/Jan/2006 (serial date type)
tauFALSE19/Jul/2005 (serial date type)
rFALSE0.10
bFALSE0.05
vFALSE0.30
GreekFALSEPREMIUM


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 TurnbullWakemanAsian() 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 TurnbullWakemanAsian() function call


9.15861157314038

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