Bond_Curve_Fit_Method__Method

Available

Corresponds to the CubicBSplinesFitting method in QuantLib.

The resulting discount factor

The number of basis functions equals the number of knots minus 4.

The number of parameters equals the number of basis functions if there is no constrain at 0. Otherwise it is less by 1.

See: McCulloch, J. 1971, "Measuring the Term Structure of Interest Rates." Journal of Business, 44: 19-31

McCulloch, J. 1975, "The tax adjusted yield curve."Journal of Finance, XXX811-30

Warning: The results are extremely sensitive to the number and location of the knot points, and there is no optimal way of selecting them.

James, J. and N. Webber, "Interest Rate Modelling" John Wiley, 2000, pp. 440

Corresponds to the ExponentialSplinesFitting method in QuantLib.

The resulting discount factor

Without the constrain, it depends on 10 parameters and has the form:

with parameter ordering:

With the constrain, it depends on 9 parameters and has the form:

where

and parameter ordering:

See: Li, B., E. DeWetering, G. Lucas, R. Brenner and A. Shapiro (2001): "Merrill Lynch Exponential Spline Model." Merrill Lynch Working Paper

Warning: Convergence may be slow.

Corresponds to the NelsonSiegelFitting method in QuantLib.

The resulting zero rate

The QuantLib implementation actually replaces the product

The parameter ordering is:

See: Nelson, C. and A. Siegel (1985): "Parsimonious modeling of yield curves for US Treasury bills." NBER Working Paper Series, no 1594.

Corresponds to the SimplePolynomialFitting method in QuantLib.

The resulting discount factor

Without the constrain, it depends on

with parameter ordering:

With the constrain, it depends on

with parameter ordering:

This is a simple/crude, but fast and robust, means of fitting a yield curve

Corresponds to the SpreadFittingMethod method in QuantLib.

Fits a spread curve on top of a discount function according to given parametric method.

The resulting discount factor

where

The denominator

The parameter ordering is that of the referenced parametric method.

Corresponds to the SvenssonFitting method in QuantLib.

The resulting zero rate

The QuantLib implementation actually replaces the productσ

The parameter ordering is:

See: Svensson, L. (1994). Estimating and interpreting forward interest rates: Sweden 1992-4. Discussion paper, Centre for Economic Policy Research(1051).