Mastering Python for Finance - Second Edition

The Brennan and Schwartz model

The Brennan and Schwartz model is a two-factor model where the short-rate reverts toward a long-term rate as the mean, which also follows a stochastic process. The short-rate process is given as follows:

It can be seen that the Brennan and Schwartz model is another form of a geometric Brownian motion.

Our Python code can now be implemented as follows:

In [ ]:    import math    import numpy as np    def brennan_schwartz(r0, K, theta, sigma, T=1., N=10, seed=777):            np.random.seed(seed)        dt = T/float(N)            rates = [r0]        for i in range(N):            dr = K*(theta-rates[-1])*dt + \                sigma*rates[-1]*math.sqrt(dt)*np.random.normal() rates.append(rates[-1] ...