# Short-Interest Rates Models - Geometric Brownian Motion?

in a paper of Brennon&Schwartz (1977), they model embedded bond options by using an stochastic interest rate model which follows a geometric Brownian Motion. Now they claim that this assumption does hold when we assume that the Pure Expectation Hypothesis holds? I do not get the link to that.

Further, what are Pros & Cos of using a Geometric Browninan Motion as an Interest Rate process, in general? What are state-of-the art models which are applied nowadays?

Greetings,

KS

• In a negative rates environment, opting for a geometric Brownian motion to model short rates will clearly pose some problems... – Quantuple Jun 21 '17 at 14:55
• There is another problem with short rate models that have a geometric diffusion term: the expected value of the money market account is infinite for any time horizon, see e.g. Chapter 3.2.2 in Brigo and Mercurio (2007) who discuss this problem for the Dothan (1978) model. – LocalVolatility Jun 22 '17 at 7:23

• $dr_t = (\mathbf{\theta(t)} - \lambda r_t) dt + \sigma(t) dt$. See for instance en.wikipedia.org/wiki/Hull%E2%80%93White_model – Antoine Conze Jun 23 '17 at 6:22