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<p>This article presents three different variable space-time grid operator splitting (OS) methods for pricing American option under jump-diffusion model. The temporal semi-discretization is done using variable time step implicit-explicit backward difference OS (BDF-OS), Crank-Nicolson OS (CN-OS), and midpoint OS (MP-OS) methods. A priori stability analysis is performed for each semi-discrete method and error estimates are established. The space discretization is performed using the variable space step finite difference approximations. The numerical illustrations for Merton’s and Kou’s jump-diffusion models are performed. The BDF-OS method is demonstrated to be first-order accurate in time and second-order accurate in space variable, while the CN-OS and MP-OS methods are second-order accurate in both the variables. The impact of the variable space-time grid is shown via error plots.</p>

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Stability and Error Estimates of Operator Splitting Methods on a Variable Space-Time Grid for American Options with Jumps

  • 期刊论文

  • 发表日期：

    2025年6月18日

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  • Pradeep Kumar Sahu,
  • Kuldip Singh Patel,
  • Pawan Kumar Mishra

摘要

This article presents three different variable space-time grid operator splitting (OS) methods for pricing American option under jump-diffusion model. The temporal semi-discretization is done using variable time step implicit-explicit backward difference OS (BDF-OS), Crank-Nicolson OS (CN-OS), and midpoint OS (MP-OS) methods. A priori stability analysis is performed for each semi-discrete method and error estimates are established. The space discretization is performed using the variable space step finite difference approximations. The numerical illustrations for Merton’s and Kou’s jump-diffusion models are performed. The BDF-OS method is demonstrated to be first-order accurate in time and second-order accurate in space variable, while the CN-OS and MP-OS methods are second-order accurate in both the variables. The impact of the variable space-time grid is shown via error plots.