Efficient pricing of interest rate derivatives under a sticky diffusion

The paper proposes a lattice-based approximation for pricing bonds and interest-sensitive claims when short-term interest rates fluctuate according to an Ornstein-Uhlenbeck process with the sticky reflecting boundary at zero. The framework is of particular interest when central banks adopt zero interest rate policies, e.g., the US monetary policy response to the financial crisis in 2008. The proposed model provides an evaluation instrument, useful for practitioners too, that is able to manage easily the sticky reflecting feature, thus avoiding to resort to the complex evaluation formulas that can arise when embedding such a feature in the considered dynamics. The underlying interest rate process is discretized through a recombining binomial lattice in which the number of nodes grows up linearly with the number of time steps. The resulting algorithm is applied to evaluate bonds and interest-sensitive claims in order to show its accuracy and efficiency.