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Drawdowns, Drawups, and Occupation Times under General Markov Models

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  • Pingping Zeng
  • Gongqiu Zhang
  • Weinan Zhang

Abstract

Drawdown risk, an important metric in financial risk management, poses significant computational challenges due to its highly path-dependent nature. This paper proposes a unified framework for computing five important drawdown quantities introduced in Landriault et al. (2015) and Zhang (2015) under general Markov models. We first establish linear systems and develop efficient algorithms for such problems under continuous-time Markov chains (CTMCs), and then establish their theoretical convergence to target quantities under general Markov models. Notably, the proposed algorithms for most quantities achieve the same complexity order as those for path-independent problems: cubic in the number of CTMC states for general Markov models and linear when applied to diffusion models. Rigorous convergence analysis is conducted under weak regularity conditions, and extensive numerical experiments validate the accuracy and efficiency of the proposed algorithms.

Suggested Citation

  • Pingping Zeng & Gongqiu Zhang & Weinan Zhang, 2025. "Drawdowns, Drawups, and Occupation Times under General Markov Models," Papers 2506.00552, arXiv.org.
    • Handle: RePEc:arx:papers:2506.00552
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    References listed on IDEAS

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    11. Cui, Zhenyu & Lee, Chihoon & Liu, Yanchu, 2018. "Single-transform formulas for pricing Asian options in a general approximation framework under Markov processes," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1134-1139.
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