Chartis Research Report Ranks Kamakura Risk Manager (Fiserv KRM) Number 1 in the World July 23, 2010 Friday Forecast: 10 Year Forecast of U.S. Treasury Yields And U.S. Dollar Interest Rate Swap Spreads Kamakura Blog: Fixed Income Performance Attribution July 16, 2010 Friday Forecast: 10 Year Forecast of U.S. Treasury Yields And U.S. Dollar Interest Rate Swap Spreads
Kamakura Blog: The Links between CDS Spreads and Default Probabilities More...
In Part 10 of this series, we present the final installment in yield curve and forward rate smoothing techniques before moving on to smoothing credit spreads. We introduce the maximum smoothness forward rate technique introduced by Adams and van Deventer (1994) and corrected in van Deventer and Imai (1996), which we call Example H. We explain why a quartic function is needed to maximize smoothness of the forward rate function over the full length of the forward rate curve, just as twice differentiable yield curve segments produce a shorter length yield curve over the full length of the curve even though the shortest length between any two points is a linear function. Finally, we compare 23 different techniques for smoothing yields and forward rates that have been discussed in this series and show why the maximum smoothness forward rate approach is the best technique by multiple criteria. Read More »
In Part 10 of this series, we present the final installment in yield curve and forward rate smoothing techniques before moving on to smoothing credit spreads. We introduce the maximum smoothness forward rate technique introduced by Adams and van Deventer (1994) and corrected in van Deventer and Imai (1996), which we call Example H. We explain why a quartic function is needed to maximize smoothness of the forward rate function over the full length of the forward rate curve, just as twice differentiable yield curve segments produce a shorter length yield curve over the full length of the curve even though the shortest length between any two points is a linear function. Finally, we compare 23 different techniques for smoothing yields and forward rates that have been discussed in this series and show why the maximum smoothness forward rate approach is the best technique by multiple criteria.
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In Part 8 of this series, we observed that it has been proven that a cubic spline, in general, produces the smoothest set of curves that one can draw between data points. This is certainly true in the case of smoothing the yield curve. As we show in part 10 of this blog series, this is NOT TRUE in the case of a cubic spline of forward rate curves if we apply the normal constraints one needs to fit observable financial data. In this post, we ignore that insight and flail ahead, erroneously assuming that if splines work reasonably well when applied to yields, they will work even better when applied to forward rates. In Example G, we apply cubic splines to forward rates and derive the related yields. The results clearly illustrate why a true “maximum smoothness” approach is needed. We deliver that approach in Part 10, which explains the full maximum smoothness approach first proposed by Adams and van Deventer in 1994. Read More »
In Part 8 of this series, we observed that it has been proven that a cubic spline, in general, produces the smoothest set of curves that one can draw between data points. This is certainly true in the case of smoothing the yield curve. As we show in part 10 of this blog series, this is NOT TRUE in the case of a cubic spline of forward rate curves if we apply the normal constraints one needs to fit observable financial data. In this post, we ignore that insight and flail ahead, erroneously assuming that if splines work reasonably well when applied to yields, they will work even better when applied to forward rates. In Example G, we apply cubic splines to forward rates and derive the related yields. The results clearly illustrate why a true “maximum smoothness” approach is needed. We deliver that approach in Part 10, which explains the full maximum smoothness approach first proposed by Adams and van Deventer in 1994.
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