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Interpolating the Yield Curve

Oldrich Alfons Vasicek
The Journal of Fixed Income Fall 2020, 30 (2) 76-85; DOI: https://doi.org/10.3905/jfi.2020.1.094
Oldrich Alfons Vasicek
is the director of Vasicek Associates and a founding partner of KMV Corporation in San Francisco, CA
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Abstract

This article proposes an interpolation (and an extrapolation to the short rate) of the yield curve between a given number of observed yields on benchmark bonds that is compatible with an arbitrage-free model of the term structure of interest rates. The model is a multivariate time-homogeneous Gaussian yield factor model. It is shown that the interpolation that minimizes the integral of the yield variance, called the maximum stability interpolation, corresponds to the case that all eigenvalues of the mean-reversion matrix of the benchmark yields are equal. Explicit equations for calculation of the maximum stability interpolation are given.

TOPIC: Factor-based models

Key Findings

  • • Explicit equations are given for interpolation of the yield curve.

  • • The equations are based on an equilibrium multifactor term structure model.

  • • A criterion for maximum stability of the interpolation is introduced.

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The Journal of Fixed Income: 30 (2)
The Journal of Fixed Income
Vol. 30, Issue 2
Fall 2020
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Interpolating the Yield Curve
Oldrich Alfons Vasicek
The Journal of Fixed Income Sep 2020, 30 (2) 76-85; DOI: 10.3905/jfi.2020.1.094

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Interpolating the Yield Curve
Oldrich Alfons Vasicek
The Journal of Fixed Income Sep 2020, 30 (2) 76-85; DOI: 10.3905/jfi.2020.1.094
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  • Article
    • Abstract
    • YIELD FACTOR MODEL
    • THE DISTINCT EIGENVALUES YIELD FACTOR MODEL
    • INTERPOLATION WITH DISTINCT EIGENVALUES
    • THE EQUAL EIGENVALUES YIELD FACTOR MODEL
    • THE EQUAL EIGENVALUES INTERPOLATION
    • THE NELSON–SIEGEL INTERPOLATION
    • REMARKS
    • ADDITIONAL READING
    • APPENDIX
    • REFERENCES
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  • PDF

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