Scholarlink

<p>This article presents the stability and error estimates of the operator splitting (OS) method for pricing American options under the regime-switching jump-diffusion model with local volatilities. The use of the discrete Gronwall lemma aids in analysis under the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-norm. The OS method combined with the implicit-explicit one and two-step backward difference formulas are utilized for temporal semi-discretization. We address the fully discrete problem using finite difference approximations. Merton and Kou jump-diffusion models under regime-switching framework are considered for pricing American put options. The efficiency and accuracy of the proposed methods are demonstrated through numerical illustrations. The <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\ell _2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ℓ</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-error at each time step is presented graphically for both models, and the overall convergence for each method is shown to be second order.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Stability and error estimates of operator-splitting methods for pricing American option under regime-switching model with jumps

  • 期刊论文

  • 发表日期：

    2025年7月23日

查看全文
  • Pradeep Kumar Sahu,
  • Kuldip Singh Patel,
  • Muddun Bhuruth

摘要

This article presents the stability and error estimates of the operator splitting (OS) method for pricing American options under the regime-switching jump-diffusion model with local volatilities. The use of the discrete Gronwall lemma aids in analysis under the \(L^2\) L 2 -norm. The OS method combined with the implicit-explicit one and two-step backward difference formulas are utilized for temporal semi-discretization. We address the fully discrete problem using finite difference approximations. Merton and Kou jump-diffusion models under regime-switching framework are considered for pricing American put options. The efficiency and accuracy of the proposed methods are demonstrated through numerical illustrations. The \(\ell _2\) ℓ 2 -error at each time step is presented graphically for both models, and the overall convergence for each method is shown to be second order.