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<p>This paper presents the stability and error analysis for the IMEX-BDF-OS techniques, which aim to solve the linear complementarity problem (LCP) for pricing American options in a Markovian regime-switching jump-diffusion (RSJD) economy. Multiple regime-switching models have been fitted with the OS schemes with favourable outcomes. The complementarity requirements and the differential equation are separated and studied independently, making it easier to apply to LCP. Nevertheless, no stability or error analysis is provided for the American option under the RSJD model by these operator-splitting procedures despite their popularity. Based on the IMEX-BDF1 and IMEX-BDF2 approaches, we estimated the error for these techniques and offered a priori stability estimates for operator splitting (OS) strategies. We numerically tested the operator splitting techniques and showed how IMEX-BDF1 and IMEX-BDF2 worked for the test issues, highlighting how well they converged.</p>

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Implicit-Explicit BDF-OS Schemes for Pricing American Style Options in Markovian Regime-Switching Economy with Jumps: An Approximation of Error

  • 期刊论文

  • 发表日期：

    2026年1月16日

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  • Deepak Kumar Yadav,
  • Akanksha Bhardwaj,
  • Gobinda Rakshit,
  • Alpesh Kumar

摘要

This paper presents the stability and error analysis for the IMEX-BDF-OS techniques, which aim to solve the linear complementarity problem (LCP) for pricing American options in a Markovian regime-switching jump-diffusion (RSJD) economy. Multiple regime-switching models have been fitted with the OS schemes with favourable outcomes. The complementarity requirements and the differential equation are separated and studied independently, making it easier to apply to LCP. Nevertheless, no stability or error analysis is provided for the American option under the RSJD model by these operator-splitting procedures despite their popularity. Based on the IMEX-BDF1 and IMEX-BDF2 approaches, we estimated the error for these techniques and offered a priori stability estimates for operator splitting (OS) strategies. We numerically tested the operator splitting techniques and showed how IMEX-BDF1 and IMEX-BDF2 worked for the test issues, highlighting how well they converged.