This is a second in a series of pricing methods, other than the normal present value of cash flows using one discount rate (yield). In the last post we considered pricing MBS, or any amortizing loan, using the U.S. Treasury spot rate Z curve.
This post takes the previous post one step further and uses the spot rates to calculate the forward curve consisting of the implied forward monthly rates from one month out to 30 years.
I used a smoothing method for the forward rates as I explain below:
I could have use a smoothing method on the initial Treasury yield curve using something like a Piecewise Cubic Spine method. This might have helped with the exaggerated forward curve. Adding to the exaggerated forward curve was the fact that I used the current Treasury curve which is relatively flat and contains unusual patterns. For example, the three year security was one basis point lower than both the two and five year securities. Also, the two month bill was higher than both the one month and three month bills.
Below shows the beginning portion of the amortization sheet that calculates price given the forward one month curve.