13.16 Choosing a Smoothing Method

One of the most fundamental steps in fixed-income option valuation is calculating a smooth yield curve. The original yield curve from the Rate Management IRC may not have enough terms for the term structure parameter estimation routine to work properly. In particular, the trinomial lattice needs the value of the yield for every bucket point.

The simple description of smoothing is to draw a smooth, continuous line through observable market data points. Because an infinite number of smooth, continuous lines pass through a given set of points, some other criterion has to be provided to select among the alternatives. There are many different ways to smooth a yield curve. The best technique is the one that results in the best term structure parameters.

The Rate Generator has two different smoothing techniques:

• Cubic Spline
• Linear Interpolation