Svensson Yield Curve Model

Overview

This repository contains an implementation of the Svensson (1994) model for yield curve fitting and analysis in R. The Svensson model extends the Nelson-Siegel approach by adding a fourth term to better capture complex yield curve shapes, making it particularly useful for fixed income analysis and interest rate modeling.

Features

• Spot Rate Calculation: Calculate spot interest rates for any maturity using calibrated Svensson model parameters
• Parameter Estimation: Fit the Svensson model parameters to observed market rates using numerical optimization
• Fixed Maturity Series Generation: Create time series of interest rates for standard fixed maturities from treasury bond data

Functions

svensson_rate()

Calculate spot interest rates using the Svensson model.

svensson_rate(t, beta0, beta1, beta2, beta3, tau1, tau2)

Parameters:

• t: Time to maturity in years
• beta0: Long-term interest rate level parameter
• beta1: Short-term component parameter
• beta2: Medium-term component parameter
• beta3: Second medium-term component parameter
• tau1: First decay parameter (must be positive)
• tau2: Second decay parameter (must be positive)

fit_svensson()

Estimate Svensson model parameters from observed market rates.

fit_svensson(maturities, rates)

Parameters:

• maturities: Numeric vector of times to maturity in years
• rates: Numeric vector of observed interest rates corresponding to maturities

generate_fixed_maturity_series()

Generate a time series of interest rates for standard fixed maturities using treasury bond data.

generate_fixed_maturity_series(dados_tesouro)

Parameters:

• dados_tesouro: Data frame with treasury bond data containing columns:
  • ref_date: Reference date
  • matur_date: Maturity date
  • yield_bid: Yield to maturity

Usage Examples

Basic Rate Calculation

# Calculate 5-year spot rate
rate <- svensson_rate(
  t = 5, beta0 = 0.04, beta1 = -0.02,
  beta2 = -0.01, beta3 = 0.005,
  tau1 = 1.5, tau2 = 4
)

Parameter Estimation

# Fit model to market data
maturities <- c(0.5, 1, 2, 5, 10)
rates <- c(0.02, 0.025, 0.03, 0.035, 0.04)
params <- fit_svensson(maturities, rates)

# Use the fitted parameters
params
# [1] beta0 beta1 beta2 beta3 tau1 tau2

Fixed Maturity Series Generation

# Assuming dados_tesouro is your treasury bond data
fixed_rates <- generate_fixed_maturity_series(dados_tesouro)

# View the first few rows
head(fixed_rates)

Installation

# Install directly from GitHub
devtools::install_github("yourusername/svensson-yield-curve")

References

Svensson, L. E. (1994). Estimating and Interpreting Forward Interest Rates: Sweden 1992-1994. NBER Working Paper Series, No. 4871.