Using MATLAB(R) and Symbolic Math Toolbox(TM) to Develop and Analyze Financial Models

These files accompany the webinar with the same title.

Description

These files introduce how Symbolic Math Toolbox™ can be used to evaluate Nelson Siegel and Svensson models, which are 2 widely used techniques for modeling yield data. We demonstrate how you can define the models in the MuPAD notebook interface and perform some basic analysis and visualization of the models. We then show how you can calculate analytical Jacobians for the models, and use these Jacobians to help speed up an optimization where model parameters are optimized such that they fit government bond data as well as possible.

You will need MATLAB®, Symbolic Math Toolbox, and Statistics Toolbox™ to run this demo.

To run this demo, execute Yield_Curve_Optimization.m. Make sure to evaluate the contents of yieldCurve_models.mn before importing variables from the notebook using getVar. You can evaluate the entire notebook by going to the 'Notebook' menu and selecting 'Evaluate All'.

• Required Products: Statistics Toolbox; Symbolic Math Toolbox
• MATLAB release: MATLAB 7.9 (2009b)

[Salman]

 

[Niall]

 

[Henry Zhu]

Thanks for your great work.

[Liam Mescall]

Great work thanks

[Alexander K]

Thanks for sharing, these files are very helpful.
I am just a beginner in the MatLab and may be mistaken, but it seems to me that there could be an error in the Nelson-Siegel and Svensson equations in yieldCurve_models.mn file.

More specifically Nelson-Siegel model is defined as:

y1 :=b0+b1*exp(-t/t1)+b2*(-t/t1)*exp(-t/t1)

while in the matlab file nelsonsiegelforward.m in finfixed folder the same model is defined as:

ForwardRate = Beta0 + Beta1*(exp(-t/Tau1)) + Beta2*(t/Tau1)*(exp(-t/Tau1)) + Beta3*(t/Tau2)*(exp(-t/Tau2)).

Please, correct me if I am mistaken.

[Alexander K]

Sorry, the ForwardRate equation that I posted was for Svensson model and here is the equation for Nelson-Siegel model:

 ForwardRate = Beta0 + Beta1*(exp(-t/Tau1)) + Beta2*(t/Tau1)*(exp(-t/Tau1))