Markov chain approximation of one-dimensional sticky diffusions

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