Abstract
In this paper we consider several methods for building the yield curve from swap rates. In particular given the complete list of swap rates, we obtain an analytic formula for the zero rate. A continuous limit of this equation is discussed and used in order to extract the continuous yield curve. In real world applications, a complete list of swap rates is rarely present, thus one needs bootstrapping' techniques. We review and compare several methods bootstrapping techniques and add some new bootstrapping techniques. This is done by using the continuous limit equation discussed in the first part of the paper and several variational models. In our experiments, we found that the new methods are better suited to reconstruct the yield curve.
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