Vasicek Interest Rate Model

What is ‘Vasicek Interest Rate Model’

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. 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

Where 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

Explaining ‘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, indicating that the interest rate will increase towards equilibrium.

Further Reading

  • Sticky reflecting Ornstein-Uhlenbeck diffusions and the Vasicek interest rate model with the sticky zero lower bound – [PDF]
  • On the resolution of the Vasicek-type interest rate model – [PDF]
  • Machine learning Vasicek model calibration with Gaussian processes – [PDF]
  • Modeling the Term-Structure of Interest Rates in the SSE with Multiple-Factor Vasicek Model [J] – [PDF]
  • Analysis of pricing European call foreign currency option under the Vasicek interest rate model – [PDF]
  • Pricing American interest rate options under the jump-extended Vasicek model – [PDF]
  • Optimal management under stochastic interest rates: the case of a protected defined contribution pension fund – [PDF]