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<p>This paper studies the fractional nonlinear volatility-option pricing model (FNVOPM) and its applications in financial markets. Key contributions include: Firstly, using the modified <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11086_Article_IEq1.gif" Format="GIF" Height="33" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(\left( \frac{G'}{G^2}\right) \)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mfrac> <msup> <mi>G</mi> <mo>′</mo> </msup> <msup> <mi>G</mi> <mn>2</mn> </msup> </mfrac> </mfenced> </math></EquationSource> </InlineEquation>-expansion method to find FNVOPM soliton solutions, revealing various solitons. Secondly, analyzing the effect of fractional-order derivative variation on the model, filling some literatures gap. Thirdly, combining the Hamiltonian structure with dynamic analysis to study FNVOPM’s behavior. Finally, verifying high-precision (error <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11086_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\(10^{-5}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>5</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>) numerical solutions by the fourth-order Runge–Kutta method. The FNVOPM outperforms the Black–Scholes model in volatility prediction, leverage effect capture, and complex market behavior analysis.</p>

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Further exploring phase portraits, Poincaré sections and chaos identification in the coupled fractional-order nonlinear model of volatility and option pricing

  • 期刊论文

  • 发表日期：

    2025年4月8日

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  • Wen Fu,
  • Peng Guo,
  • Jianming Qi

摘要

This paper studies the fractional nonlinear volatility-option pricing model (FNVOPM) and its applications in financial markets. Key contributions include: Firstly, using the modified \(\left( \frac{G'}{G^2}\right) \) G ′ G 2 -expansion method to find FNVOPM soliton solutions, revealing various solitons. Secondly, analyzing the effect of fractional-order derivative variation on the model, filling some literatures gap. Thirdly, combining the Hamiltonian structure with dynamic analysis to study FNVOPM’s behavior. Finally, verifying high-precision (error \(10^{-5}\) 10 - 5 ) numerical solutions by the fourth-order Runge–Kutta method. The FNVOPM outperforms the Black–Scholes model in volatility prediction, leverage effect capture, and complex market behavior analysis.