By Donald van Deventer on
12/10/2009 12:09 PM
In this post we make an important change in our definition of the “best yield curve.” In this post we change the definition of “best” to be the yield curve with “maximum smoothness,” which we define mathematically. Given the other constraints we impose for realism, we find that this definition of “best” implies that yield curve should be formed from a series of cubic polynomials. We then turn to Example F, in which we apply cubic splines to yields and derive the related forward rates. We compare the result to Example E, the quadratic spline of forward rates, and we draw some interesting conclusions. We then lay out our plans for Part 9 in the series, a cubic spline of forward curves.
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By Donald van Deventer on
12/8/2009 1:50 PM
In this post we take a logical step forward from Example D in part 6 of this series, where we used quadratic splines to fit yields. The result of that exercise was two insights. First we saw much more variation in forward rates than yields, and we found that the “right hand” side constraint on the “best yield curve” can have a big impact on the nature of both yields and forwards. In this post, we turn to Example E, in which we apply quadratic splines to forward rates. The result is a big improvement in realism, which is the ultimate criterion for “best yield curve.” We close by making our normal comparison to the misused Nelson-Siegel technique and lay out our plans for Part 8 in the series, “maximum smoothness yield curves.”
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By Donald van Deventer on
12/4/2009 12:07 PM
President Obama’s pay czar Kenneth Feinberg has a daunting task. He has to intervene and override “market forces” to establish “fair pay” for the CEOs of major institutions that are reliant on government support for their survival. The difficulty in this process is a simple fact: football coaches are paid for their skill, but large company CEOs are not. Large company CEOs, with a few exceptions, are winners of a lottery that entitles them to huge payouts during their brief tenure. On behalf of the shareholders, the Boards of Directors of these firms have to do a better job of separating luck from skill.
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By Donald van Deventer on
12/3/2009 1:34 PM
In Part 6 of our series on the basic building blocks of yield curve smoothing, we learn from our results in Part 5 (linear forward rates). We found in Part 5 that, for forward rates to be continuous and linear, we induced too much of a saw-tooth pattern in forward rates, even though the yields implied by these forward rates looked reasonable. In this post, we turn to Example D, in which we seek to “take the teeth out of the saw tooth pattern” by requiring that the first derivatives of the curve segments we fit be equal at the knot points. We use a quadratic spline of yields to achieve this objective, and we optimize to produce the “maximum tension/minimum length” yields and forwards consistent with the quadratic splines. Finally, we compare the results to the popular but flawed Nelson-Siegel approach and gain still more insights on how to further improve the realism of our smoothing techniques.
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By Donald van Deventer on
11/30/2009 12:03 PM
In Part 5 of our series on the basic building blocks of yield curve smoothing, we make another adjustment of the constraints we’ve imposed on the “best” yield curve. We find that our criterion for best implies linear segments for forward rates, as in the linear yield example in Part 4. The related yields, however, are not linear. The other difference in Example C, which we explain here, is that we require the forward rates to be continuous to avoid the unrealistic jumps in forward rates at the knot points which we saw in Example B, the case of linear yields. We again compare the results to the popular but flawed Nelson-Siegel approach and gain still more insights on how to further improve the realism of our smoothing techniques.
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