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Modeling Nelson-Siegel Yield Curve using Bayesian Approach

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  • Sourish Das

Abstract

Yield curve modeling is an essential problem in finance. In this work, we explore the use of Bayesian statistical methods in conjunction with Nelson-Siegel model. We present the hierarchical Bayesian model for the parameters of the Nelson-Siegel yield function. We implement the MAP estimates via BFGS algorithm in rstan. The Bayesian analysis relies on the Monte Carlo simulation method. We perform the Hamiltonian Monte Carlo (HMC), using the rstan package. As a by-product of the HMC, we can simulate the Monte Carlo price of a Bond, and it helps us to identify if the bond is over-valued or under-valued. We demonstrate the process with an experiment and US Treasury's yield curve data. One of the interesting observation of the experiment is that there is a strong negative correlation between the price and long-term effect of yield. However, the relationship between the short-term interest rate effect and the value of the bond is weakly positive. This is because posterior analysis shows that the short-term effect and the long-term effect are negatively correlated.

Suggested Citation

  • Sourish Das, 2018. "Modeling Nelson-Siegel Yield Curve using Bayesian Approach," Papers 1809.06077, arXiv.org, revised Oct 2018.
    • Handle: RePEc:arx:papers:1809.06077
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    5. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    6. Das, Sourish & Dey, Dipak K., 2006. "On Bayesian Analysis of Generalized Linear Models Using the Jacobian Technique," The American Statistician, American Statistical Association, vol. 60, pages 264-268, August.
    7. Das, Sourish & Dey, Dipak K., 2010. "On Bayesian inference for generalized multivariate gamma distribution," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1492-1499, October.
    8. Sourish Das & Dipak K. Dey, 2013. "On Dynamic Generalized Linear Models with Applications," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 407-421, June.
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