Vasicek Interest Rate Model

What is the 'Vasicek Interest Rate Model'

The Vasicek interest rate model is a method of modeling interest rate movement that describes the movement of an interest rate as a factor of market risk, time and equilibrium value that the rate tends to revert towards. Essentially, it predicts where interest rates will end up at the end of a given period of time given current market volatility, the long-run mean interest rate value, and a given market risk factor. It is important to note that the equation can only test one market risk factor at a time. This stochastic model is often used in the valuation of interest rate futures.

The Vasicek interest rate model values the instantaneous interest rate using the following equation:

drt = a(b-rt)dt +sdWt

Wt is the random market risk (represented by the Wiener process)
t represents time
a(b-rt) represents the expected change in the interest rate at t (drift factor)
a is the speed of reversion
b is the long-term level of the mean
s is the volatility at the time

BREAKING DOWN 'Vasicek Interest Rate Model'

The Vasicek interest rate model states that the movement of interest rates is affected only by random market movements. In the absence of market shocks (i.e., when dWt = 0) the interest rate remains constant (rt = b). When rt < b, the drift factor becomes positive, it indicates that the interest rate will increase toward equilibrium. Although it was a great step forward in predictive equations, the main drawback of the model that has come to light since the global financial crisis is that the Vasicek model does not allow interest rates to dip below zero. This issue has been fixed in several models that have been developed since the Vasicek model such as the exponential Vasicek model and the Cox-Ingersoll-Ross model.