Term structure of interest rates with stickiness: a subdiffusion approach

Abstract

In this paper, we propose a new class of term structure of interest rate models which is built on the subdiffusion processes. We assume that the spot rate is a function of a time changed diffusion process belonging to a symmetric pricing semigroup for which its spectral representation is known. The time change process is taken to be an inverse Levy subordinator in order to capture the stickiness feature observed in the short-term interest rates. We derive the analytical formulas for both bond and bond option prices based on eigenfunction expansion method. We also numerically implement a specific subdiffusive model by testing the sensitivities of bond and bond option prices with respect to the parameters of time change process.