Term Structure Analytics

What the platform does

This edition estimates yield curves from effective market observations already embedded in the site.

It combines three complementary curve-construction approaches:

• Classic Nelson-Siegel: fits level, slope and curvature factors by date.
• Nelson-Siegel-Svensson: extends Nelson-Siegel with a second curvature factor.
• Cubic spline: interpolates a smooth curve directly across the observed nodes.

Data architecture

The platform operates exclusively with effective market data.

• Embedded dataset: uses a real market dataset preloaded inside the static site.
• Legacy aliases: names such as spc_pesos_2y are normalized into SPC_2Y.

In this edition, the full dataset is shipped with the site and all computation runs in the browser, with no operational backend dependency.

Normalization and cleaning

Before estimation, the platform:

• converts Date into a usable time index
• casts rate columns to numeric values
• preserves real gaps as NaN
• uses only complete dates for the selected columns

Curves are estimated on the cleaned dataset displayed in the Data tab.

Methodological framework

• takes a cross-section of rates by date
• builds level, slope and curvature loadings
• uses a fixed lambda = 0.0609, matching the original notebook
• estimates betas through least squares
• reconstructs a continuous curve across maturity

• adds a fourth curvature factor
• uses two lambda parameters
• estimates betas through least squares

• uses only the available observed rates
• fits a natural cubic interpolation
• produces a smooth curve without latent factors

How to read the charts

• Observed yields: effective market points available on the selected date.
• Estimated curve: fitted model line.
• Factors: historical evolution of the estimated parameters.

Baseline curve projection

The Projection tab uses the historical Nelson-Siegel factors and fits a separate AR(1) process for level, slope and curvature.

• each factor is modeled with first-order persistence
• 1M, 3M, 6M and 12M horizons are approximated with daily market steps
• the forward curve is rebuilt from the expected betas at the selected horizon

Dynamic Nelson-Siegel with Kalman

The Kalman tab keeps the Nelson-Siegel measurement structure but treats the factors as latent states and smooths them over time with a Kalman filter and smoother.

• the measurement equation maps Nelson-Siegel loadings into the observed yield cross-section
• the transition equation uses a diagonal AR(1) persistence as a parsimonious baseline
• the output is a filtered spot curve and a consistent filtered forward curve for each date