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<p>This paper presents the impact of liquidity shocks on American option pricing using a nonlinear complementarity problem. The operator splitting technique approximates the nonlinear complementarity problem, which gives rise to a degenerate parabolic-ordinary system. Implicit-explicit (IMEX) methods are used to solve the degenerate parabolic-ordinary system. Theoretical results for the positivity of the solution of the parabolic-ordinary system are established using the comparison principle. Convergence analysis and the comparison principle are also demonstrated for the discretized system. Numerical experiments on uniform and nonuniform meshes validate the accuracy and efficiency of the proposed methods, matching the theoretical findings.</p>

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Numerical valuation of American options with liquidity shocks using IMEX methods

  • 期刊论文

  • 发表日期：

    2025年6月28日

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  • Ankit Singh,
  • Vikas Maurya,
  • Manoj K. Rajpoot

摘要

This paper presents the impact of liquidity shocks on American option pricing using a nonlinear complementarity problem. The operator splitting technique approximates the nonlinear complementarity problem, which gives rise to a degenerate parabolic-ordinary system. Implicit-explicit (IMEX) methods are used to solve the degenerate parabolic-ordinary system. Theoretical results for the positivity of the solution of the parabolic-ordinary system are established using the comparison principle. Convergence analysis and the comparison principle are also demonstrated for the discretized system. Numerical experiments on uniform and nonuniform meshes validate the accuracy and efficiency of the proposed methods, matching the theoretical findings.