Term structure estimation with liquidity-adjusted Affine Nelson Siegel model: A nonlinear state space approach applied to the Indian bond market

Harvesting the volatility smile in a large emerging market: A Dynamic Nelson–Siegel approach

“…Diebold and Li (2006) extended the NS model into a dynamic setting by allowing the NS parameters to vary over time. Referred to as the DNS model, its popularity has only increased since (for a recent survey, see Kumar & Virmani, 2022). The dynamics of the spot rate in the DNS model is given by…”

“…Diebold and Li (2006) extended the NS model into a dynamic setting by allowing the NS parameters to vary over time. Referred to as the DNS model, its popularity has only increased since (for a recent survey, see Kumar & Virmani, 2022). The dynamics of the spot rate in the DNS model is given by $$${y}_{t}(\tau )={\beta }_{0,t}+{\beta }_{1,t}\left(\frac{1-{e}^{-\lambda \tau }}{\lambda \tau }\right)+{\beta }_{2,t}\left(\frac{1-{e}^{-\lambda \tau }}{\lambda \tau }-{e}^{-\lambda \tau }\right),$$$ where $${y}_{t}$$ is the zero‐coupon yield at time $$t$$ with maturity $$\tau $$, and $${\beta }_{0,t},{\beta }_{1,t},{\beta }_{2,t}$$ are often referred to as “factor loadings” (Nelson & Siegel, 1987).…”

“…We cast our dynamic models in a state‐space framework and estimate them using the approach laid out in Kumar and Virmani (2022). We describe the steps for estimation for the DNS model here.…”