![]() However, in most cases, NS model is sufficiently good fitting results. The following R code estimates parameters of NSS model with yield curves at four dates and compares these results with that of NS model. However, reasonable constrains on two decay parameters are dependent on which data is used. I set two ranges of maturities as 1 ~ 5 years and 6 ~ 20 year for example. It is typical to determine \(\lambda_1\) from ranges of medium-term maturities and \(\lambda_2\) from ranges of long-term maturities. Without suitable restrictions on these two parameters, estimates of these parameters exhibit too excessive or erratic. The most difficult part of the estimation of NSS model is how to choose \(\lambda_1\) and \(\lambda_2\). Restrictions on \(\lambda_1\) and \(\lambda_2\) ![]() For this reason too small \(\lambda_2\) is not appropriate and is needed to be constrained by some reasonable upper and lower bounds. Smaller \(\lambda_2\) fits the yield curve at longer maturities well but it lowers the interpretability of the level factor. In the above figure, I use \(\lambda_1 = 0.0609\) and \(\lambda_2 = 0.01 \), which represent the maximum of curvature loadings are attained at nearly 30-month and 180-month respectively. \(\lambda_1\) and \(\lambda_2\) determine the shapes of slope and two curvature factor loadings as follows. \(\lambda_1\) and \(\lambda_2 \) are the decay parameters. \(\beta_1, \beta_2, \beta_3\, \beta_4\) are coefficient parameters. Here, \(\tau\) is a maturity and \(y(\tau)\) is a continuously compounded spot rate with \(\tau\) maturity. Nelson-Siegel model is a non-linear least square problem with 6 parameters with some inequality constraints. ![]() Bayesian Estimation by using rjags R Package.Excel Solver using VBA macro : Nelson-Siegel yield curve fitting.Non-linear Optimization of Nelson-Siegel model using nloptr R package.Non-linear Optimization by using R function. ![]() Written by one of the leading names in the fixed income markets today, this book should prove to be an invaluable reference guide for all those with an interest in corporate bond markets, whether as practitioners, consultants or researchers. It also discusses the analysis of these instruments. The book covers the full set of instruments used by companies to raise finance, and which are aimed at a wide range of investors. There is background information on bond pricing and yield, as well as a detailed look at the yield curve. This book is a detailed account of the instruments that are used in the corporate bond markets, from conventional "plain vanilla" bonds to hybrid instruments and structured products. ![]()
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