Markov chain approximation of one-dimensional sticky diffusions. (June 2021)

• Record Type: Journal Article
• Authors: Meier, Christian; Li, Lingfei; Zhang, Gongqiu
• Is Part Of: Advances in applied probability. Volume 53:Number 2(2021)
• Page Start: 335
• Page End: 369
• Publication Date: 2021-06
• Subjects: Diffusions -- sticky boundary -- Markov chain approximation -- simulation -- Sturm–Liouville problem; 65C40 -- 60J60 -- 65C05 -- 34L10 -- 34L16; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2020.65
• Languages: English
• ISSNs: 0001-8678

Abstract

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 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 a low-interest environment and option pricing under a geometric Brownian motion price model with a sticky interior point.