  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.
