Bond Pricing Based on Nelson-Siegel Model
Bond Pricing Based on Nelson-Siegel Model
——An Analysis of Varied Parameter τ
Introduction
Nelson and Siegel (1987) suggest to fit the forward rate curve at a given date with a mathematical class of approximating functions. The model precisely reflects the expected YTM with a flexible yield curve in the Term Structure Theorem. In this paper, we test the fitness of NS model and try to evaluate how deeply the NS model performs with different types of bonds via sampling and comparasion. We focus on the effects of parameter τ’ changing to analysis NS model.
Model explanation
The functional form Nelson and Siegel advocate uses Laguerre functions which consist of the product between a polynomial and an exponential decay term. The three components in NS model have a clear interpretation for short, medium and long-term components. These labels are the result of each element’s contribution to the yield curve. Basic model:
Where x is a vector parameter, τ is a time constant and f(t, x) donates forward interest rate in time t.
By average the equation we get the YTM. Which donated by R(x, t),
Later, in order to run the regression, we use OLS methods to minimize the sum square of interest rate spread.
That can also be written as this form:
Notice that there are only 4 factors in the final model, which gives a very high flexibility to the research process.
The model shows the forward and yield curves which have the desirable property of starting off from an easily computed instantaneous short rate value of β0+β1, t and leveling off at a finite infinite-maturity value of β0, that is constant: lim R(t, x)(τ) = β0 + β1; τ→0 lim R(t, x)(τ) = β0 τ→∞ Data
The data collected to test how well NS model performs in estimating the term structure of interest rate is 165 pieces of zero-coupon bonds issued in the U.S. on April 11th 2014. After graphing the real YTM scatter diagram, we found that these bonds’ YTMs are monotone increasing basically.
We thus assume
——An Analysis of Varied Parameter τ
Introduction
Nelson and Siegel (1987) suggest to fit the forward rate curve at a given date with a mathematical class of approximating functions. The model precisely reflects the expected YTM with a flexible yield curve in the Term Structure Theorem. In this paper, we test the fitness of NS model and try to evaluate how deeply the NS model performs with different types of bonds via sampling and comparasion. We focus on the effects of parameter τ’ changing to analysis NS model.
Model explanation
The functional form Nelson and Siegel advocate uses Laguerre functions which consist of the product between a polynomial and an exponential decay term. The three components in NS model have a clear interpretation for short, medium and long-term components. These labels are the result of each element’s contribution to the yield curve. Basic model:
Where x is a vector parameter, τ is a time constant and f(t, x) donates forward interest rate in time t.
By average the equation we get the YTM. Which donated by R(x, t),
Later, in order to run the regression, we use OLS methods to minimize the sum square of interest rate spread.
That can also be written as this form:
Notice that there are only 4 factors in the final model, which gives a very high flexibility to the research process.
The model shows the forward and yield curves which have the desirable property of starting off from an easily computed instantaneous short rate value of β0+β1, t and leveling off at a finite infinite-maturity value of β0, that is constant: lim R(t, x)(τ) = β0 + β1; τ→0 lim R(t, x)(τ) = β0 τ→∞ Data
The data collected to test how well NS model performs in estimating the term structure of interest rate is 165 pieces of zero-coupon bonds issued in the U.S. on April 11th 2014. After graphing the real YTM scatter diagram, we found that these bonds’ YTMs are monotone increasing basically.
We thus assume