Svenssonmodel

The Svensson model is a parametric method for modeling the term structure of interest rates and fitting the yield curve. It is an extension of the Nelson–Siegel framework, named after Swedish economist Lars E.O. Svensson, who popularized the approach in the 1990s. The model aims to provide a flexible yet compact representation of the entire yield curve with a small number of parameters.

The instantaneous forward rate in the Svensson model is given by f(τ) = β0 + β1 e^(-τ/λ1) + β2 (τ/λ1) e^(-τ/λ1) + β3 (τ/λ2) e^(-τ/λ2), where τ is maturity. The corresponding zero-coupon yield z(τ) has a closed-form expression: z(τ) = β0 + β1 [(1 − e^(-τ/λ1)) / (τ/λ1)] + β2 {[(1 − e^(-τ/λ1)) / (τ/λ1)] − e^(-τ/λ1)} + β3 {[(1 − e^(-τ/λ2)) / (τ/λ2)] − e^(-τ/λ2)}. The parameters β0, β1, β2, and β3 control the level, slope, and curvature of the curve, while λ1 and λ2 are decay parameters that set the rates of the two exponential components.

Estimation methods commonly involve fitting the model to observed yields across maturities using nonlinear least squares or, in dynamic settings, Kalman filtering (dynamic Nelson–Siegel–Svensson). The model is widely used by central banks and financial institutions to produce smooth, interpretable yield curves for pricing, risk management, and policy analysis.

Originating in the work of Svensson in the 1990s, the model builds on the Nelson–Siegel specification to capture hump-shaped term structures more flexibly. It is valued for its balance of interpretability, computational efficiency, and good empirical fit, though it can be susceptible to overfitting and may not guarantee arbitrage-free conditions in all applications.