  In this paper, we argue that some of the most popular short-term interest
models have to be revisited and modified to reflect current market conditions
better. In particular, we propose a modification of the popular
Black-Karasinski model, which is widely used by practitioners for modeling
interest rates, credit, and commodities. Our adjustment gives rise to the
stochastic Verhulst model, which is well-known in the population dynamics and
epidemiology as a logistic model. We demonstrate that the Verhulst model's
dynamics are well suited to the current economic environment and the Fed's
actions. Besides, we derive new integral equations for the zero-coupon bond
prices for both the BK and Verhulst models. For the BK model for small
maturities up to 2 years, we solve the corresponding integral equation by using
the reduced differential transform method. For the Verhulst integral equation,
under some mild assumptions, we find the closed-form solution. Numerical
examples show that computationally our approach is significantly more efficient
than the standard finite difference method.
