Mastering Python for Finance - Second Edition

The Vasicek model

In the one-factor Vasicek model, the short-rate is modeled as a single stochastic factor:

Here, K, θ, and σ are constants, and σ is the instantaneous standard deviation. W(t) is the random Wiener process. The Vasicek follows an Ornstein-Uhlenbeck process, where the model reverts around the mean, θ, with K, the speed of mean reversion. As a result, the interest rates may become negative, which is an undesirable property in most normal economic conditions.

To help us understand this model, the following code generates a list of interest rates:

In [ ]:    import math    import numpy as np def vasicek(r0, K, theta, sigma, T=1., N=10, ...