Markov Chain Approximation of One-Dimensional Sticky Diffusions

TL;DR

This paper introduces a new CTMC approximation method for one-dimensional sticky diffusions, providing efficient computation of key quantities and superior simulation performance over Euler schemes, with applications in bond pricing.

Contribution

It develops a second-order convergent CTMC scheme for sticky diffusions and demonstrates its effectiveness in pricing and simulation tasks.

Findings

Second order convergence of the proposed scheme.

Efficient computation of matrix exponentials.

Improved simulation accuracy over Euler methods.

Abstract

We develop continuous time Markov chain (CTMC) approximation of one-dimensional diffusions with a lower sticky boundary. Approximate solutions to the action of the Feynman-Kac operator associated with a sticky diffusion and first passage probabilities are obtained using matrix exponentials. We show how to compute matrix exponentials efficiently and prove that a carefully designed scheme achieves second order convergence. We also propose a scheme based on CTMC approximation for the simulation of sticky diffusions, for which the Euler scheme may completely fail. The efficiency of our method and its advantages over alternative approaches are illustrated in the context of bond pricing in a sticky short rate model for low interest environment.