![]() ![]() 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. ![]()
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