Financial mathematics - estimating a yield curve

[sorensen]

The problem is to estimate a zero-coupon yield curve for up to 5 years ahead, knowing (for time t=0) the following:
bond 1: coupon 6.5, maturity - 1 year, price = 103
bond 2: coupon 5, maturity - 2 years, price = 102
bond 3: coupon 4.2, maturity - 3 years, price = 100
bond 4: coupon 6.5, maturity - 4 years, price = 104
bond 5: coupon 5.2, maturity - 5 years, price = 99
price of a 1-week treasury bill of face value=100, is 99.94

I have digged through several papers on modelling yield curves and still am stuck. Given the relatively not-advanced-at-all mathematical prerequisites needed for the financial maths class I'm attending, i shyly presume that i should use a Nelson-Siegel-Svensson model here. Then - please correct me if I'm wrong - the task in fact is to solve an optimization problem of finding the parameters that generate theoretical prices for the given bonds and a bill that are the closest to their given market prices (using some MSE or RMSE estimator i guess).

How to implement that however is a mystery for me. Are such problems to be solved in some sophisticated maths software? Since the optimization problem here is non-linear i think it can't be 'treated' by Excel Solver (which i happen no to have anyway)?

I'd be thankful for any hint about this.

And by the way please excuse me for my lousy foreigner-vocabulary. ;)

 

[lippyka]

Yes, you are correct in your assessment that you will need to use a Nelson-Siegel-Svensson model here. You can use Excel Solver if you have it, as long as you are able to define the objective and constraints properly. You may need to use the nonlinear solver though, as the nonlinear nature of the problem means it won't be solved by the linear solver alone. Alternatively, you can use a more sophisticated math software such as MATLAB or R for this task.