Retrieving Svensson's model parameters - On what order are these parameters provided?

After creating a Svensson model I would like to store the parameters calculated by the fitSvensson function.

I already know I can get the six parameters (Beta0, Beta1, Beta2, Beta3, Tau1, Tau2) from the model's "Parameters" attribute but I have no idea about on what order are these parameters provided. I searched the documentation but up to this time I found no reference to this information.

The example (below - and _ here _) doesn't help very much.

Settle = repmat(datenum('30-Apr-2008'),[6 1]);
Maturity = [datenum('07-Mar-2009');datenum('07-Mar-2011');...
datenum('07-Mar-2013');datenum('07-Sep-2016');...
datenum('07-Mar-2025');datenum('07-Mar-2036')];

CleanPrice = [100.1;100.1;100.8;96.6;103.3;96.3];
CouponRate = [0.0400;0.0425;0.0450;0.0400;0.0500;0.0425];
Instruments = [Settle Maturity CleanPrice CouponRate];
PlottingPoints = datenum('07-Mar-2009'):180:datenum('07-Mar-2036');
Yield = bndyield(CleanPrice,CouponRate,Settle,Maturity);

SvenssonModel = IRFunctionCurve.fitSvensson('Zero',datenum('30-Apr-2008'),Instruments);

SvenssonModel.Parameters
ans =

      0.0002    3.7616  -24.5489   34.3165   10.8867   11.9282

Which one is Beta1? Which one is Tau2? Any clues?

Thank you in advance and Merry Christmas to all of you!

Fernando

[Luiz Fernando Carnot R de Almeida]

After trying to figure which parameter corresponds to each of Svensson's Betas and Taus (without success) I found out that the formula presented in Mathworks's URL doesn't match Svensson's formula.

The following formula (the one @ http://www.mathworks.com/help/fininst/fitsvenssonirfunctioncurve.html)

seems to be different from the next one (the original Svensson's formula)

The differences are on some minus signs.

Am I missing something?

Any help will be appreciated.

Fernando

[Luiz Fernando Carnot R de Almeida]

I tried to use the parameters in the following order: Beta0, Beta1, Beta2, Beta3, Tau1 and Tau2.

In the original formula the results found are different from those calculated by the getZeroRates method on my SvenssonModel.

Using the formula presented in Mathworks' URL the results don't make any sense.

I also tried other parameter combinations but the results got even worse. It seems that either I am unable to find the right combination of the parameters or the formula used to calculate the zero rate is a bit different from each of the formulas in the previous comment.

[Gokturk]

Hi, Im trying to get parameters but receiving an error 'No appropriate method, property, or field Parameters for class IRFunctionCurve' can you pls help me on that thnks

Answer 1

[Luiz Fernando Carnot R de Almeida]

According to the source code (IRFunctionCurve.m):

% The fitted parameters can be recovered from the Parameters % field and are the following: (Beta0, Beta1, Beta2, Beta3, % Tau1, Tau2)

[Luiz Fernando Carnot R de Almeida]

The problem is solved.

Do not pay attention to the "Svenson's function" provided in MatLab's online documentation. Use the original one. It works.

Furthermore, bear in mind that each unity of maturity corresponds to a full year, so if you plan to calculate the interest rate of a single day and your basis is BUS/252 make sure your maturity parameter is 1/252.

Hope this helps.