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<p>A numerical method for resolving the time-fractional Black-Scholes partial-integro differential equation (PIDE) that emerges in the jump-diffusion model is presented in this article. The conventional <i>L</i>1–scheme discretises the fractional derivative in time. The spatial derivative is discretised using the non-symmetric interior penalty Galerkin (NIPG) method, and the integral component is discretised using the composite trapezoidal rule. Additionally, the outcomes of convergence and stability are demonstrated. The effect of the fractional derivative on the option price is demonstrated, and the theoretical estimates are validated using numerical experiments for both the Merton and Kou models.</p>

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Pricing of options over time-fractional Black-Scholes jump-diffusion model with the methodology of NIPG

  • 期刊论文

  • 发表日期：

    2025年4月25日

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  • K. Jaspreet,
  • S. Natesan

摘要

A numerical method for resolving the time-fractional Black-Scholes partial-integro differential equation (PIDE) that emerges in the jump-diffusion model is presented in this article. The conventional L1–scheme discretises the fractional derivative in time. The spatial derivative is discretised using the non-symmetric interior penalty Galerkin (NIPG) method, and the integral component is discretised using the composite trapezoidal rule. Additionally, the outcomes of convergence and stability are demonstrated. The effect of the fractional derivative on the option price is demonstrated, and the theoretical estimates are validated using numerical experiments for both the Merton and Kou models.