I need to do yield curve extraction for fixed income. I have 10 fixed income instruments for which I have values.
The method is called Nelson-Siegel Method: http://en.wikipedia.org/wiki/Fixed-income_attribution
The equation is $y\left( m \right) = \beta _0 + \beta _1\frac{{\left[ {1 - \exp \left( { - m/\tau} \right)} \right]}}{m/\tau} + \beta _2 {\left(\frac{{\left[ {1 - \exp \left( { - m/\tau} \right)} \right]}}{m/\tau} - \exp \left( { - m/\tau}\right)\right)} $
I need to optimize the value of tau and the betas. This is basically OLS problem. Not sure which optimizer in Matlab and how to solve this problem. Need some guidance on solving this problem.