Since there are only a finite number of bonds available in the market. There will always be "holes" to fill in when defining a yield curve in continuous time. A common approach is to define a parameterized set of possible yield curves, and choose a curve within this set that provides a good approximation of the yields of observed bonds. There are many ways to choose such a parameterized set and to define what is meant by a "good approximation." You can read a book on term structure estimation if you are interesting in learning more.

In this exercise, we will use the Nelson-Siegel parametric class of term structures.

The Nelson - Siegel model defines a set of zero-coupon yield curves, defined by five parameters, as described in class, i.e., the yield of a zero coupon bond of maturity T is y(T|A), where A={β₁,β₂,β₃,λ₁,λ₂}. The model has been covered in class.