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Simulation of multidimensional diffusions with sticky boundaries via Markov chain approximation

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  • Meier, Christian
  • Li, Lingfei
  • Zhang, Gongqiu

Abstract

In this study, we develop a novel method to simulate multidimensional diffusions with sticky boundaries for which the Euler scheme fails. We approximate the sticky diffusion process by a multidimensional continuous-time Markov chain (CTMC) that can be easily simulated. We provide two approaches to construct the CTMC. In the first approach, we approximate the infinitesimal generator of the sticky diffusion by finite difference using standard coordinate directions. In the second one, we match the local moments using the drift and the eigenvectors of the covariance matrix as transition directions. The first approach does not always guarantee a valid Markov chain, whereas the second one can. We show that both construction methods yield a first-order simulation scheme, which can capture the sticky behavior and is free from the curse of dimensionality. As applications, we use our method to simulate the limit of a queuing system with exceptional service policy and a multi-factor short rate model for low interest rate environment.

Suggested Citation

  • Meier, Christian & Li, Lingfei & Zhang, Gongqiu, 2023. "Simulation of multidimensional diffusions with sticky boundaries via Markov chain approximation," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1292-1308.
    • Handle: RePEc:eee:ejores:v:305:y:2023:i:3:p:1292-1308
    DOI: 10.1016/j.ejor.2022.07.038
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    References listed on IDEAS

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    1. Gongqiu Zhang & Lingfei Li, 2019. "Analysis of Markov Chain Approximation for Option Pricing and Hedging: Grid Design and Convergence Behavior," Operations Research, INFORMS, vol. 67(2), pages 407-427, March.
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    8. Kirkby, J. Lars & Nguyen, Dang H. & Nguyen, Duy, 2020. "A general continuous time Markov chain approximation for multi-asset option pricing with systems of correlated diffusions," Applied Mathematics and Computation, Elsevier, vol. 386(C).
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    Cited by:

    1. Zhang, Gongqiu & Li, Lingfei, 2023. "A general method for analysis and valuation of drawdown risk," Journal of Economic Dynamics and Control, Elsevier, vol. 152(C).
    2. Akihiro Kaneko, 2023. "Multi-stage Euler-Maruyama methods for backward stochastic differential equations driven by continuous-time Markov chains," Papers 2311.08826, arXiv.org, revised Nov 2023.
    3. Yeda Cui & Lingfei Li & Gongqiu Zhang, 2024. "Pricing and hedging autocallable products by Markov chain approximation," Review of Derivatives Research, Springer, vol. 27(3), pages 259-303, October.

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