State-dependent jump sizes and the Markov property in short-rate models

Investigate short-rate models with stochastic discontinuities in which the jump magnitude at each fixed jump time depends on the current level of the risk-free rate, and ascertain whether and under what conditions the resulting interest-rate process retains the Markov property required by the pricing framework.

Background

Within affine short-rate models that include square-root diffusion terms (CIR-type), maintaining non-negativity across jump times typically forces the jump sizes to be non-negative. The authors note that one way to avoid this restriction is to allow the jump sizes to depend on the current level of the risk-free rate.

However, they caution that such state-dependent jumps may compromise the Markov property, which is central to their PDE and pricing framework. The detailed analysis of this extension—how to model state-dependent jump sizes and whether the Markov property can be preserved—is not developed in the paper and is deferred to future research.