Simulating Mean-Reverting Interest Rates with the Vasicek Model

Summary

The article introduces the Vasicek model as a one-factor stochastic model for short-term interest rates. Its drift pulls rates toward a long-run mean at a speed set by the reversion parameter, while Brownian shocks create random fluctuations. It gives the model’s analytical solution and describes its long-run variance, then presents Euler–Maruyama discretisation for generating sample paths and a Monte Carlo routine for producing multiple simulations.

The discussion connects the model to fixed-income applications, including bond and interest-rate derivative pricing, term-structure analysis, and risk assessment. The simulation illustrates how paths can be generated and plotted; it does not provide empirical calibration or pricing results. The model is tractable and mean-reverting, but its constant volatility assumption and ability to produce negative rates limit its realism in some settings. The article notes that more flexible alternatives, such as the CIR model, address some of these shortcomings.

Key ideas

• The Vasicek model combines mean-reverting drift with normally distributed stochastic shocks.
• Its parameters determine the long-run rate, reversion speed, and volatility of short-rate movements.
• Euler–Maruyama discretisation can generate sample paths, and repeated simulations produce a Monte Carlo ensemble.
• The model has an analytical solution and a finite long-run variance under its assumptions.
• Constant volatility and possible negative rates are important limitations.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.