Vasicek Model - Discussion

Discussion

Vasicek's model was the first one to capture mean reversion, an essential characteristic of the interest rate that sets it apart from other financial prices. Thus, as opposed to stock prices for instance, interest rates cannot rise indefinitely. This is because at very high levels they would hamper economic activity, prompting a decrease in interest rates. Similarly, interest rates can not decrease below 0. As a result, interest rates move in a limited range, showing a tendency to revert to a long run value.

The drift factor represents the expected instantaneous change in the interest rate at time t. The parameter b represents the long run equilibrium value towards which the interest rate reverts. Indeed, in the absence of shocks, the interest remains constant when r_t = b. The parameter a, governing the speed of adjustment, needs to be positive to ensure stability around the long term value. For example, when r_t is below b, the drift term becomes positive for positive a, generating a tendency for the interest rate to move upwards (toward equilibrium).

The main disadvantage is that, under Vasicek's model, it is theoretically possible for the interest rate to become negative, an undesirable feature. This shortcoming was fixed in the Cox–Ingersoll–Ross model, exponential Vasicek model, Black–Derman–Toy model and Black–Karasinski model, among many others. The Vasicek model was further extended in the Hull–White model. The Vasicek model is also a canonical example of the affine term structure model, along with the Cox–Ingersoll–Ross model.