Modeling anomalous diffusion and volatility in the Australian national electricity market using a space-fractional Black-Scholes framework

Doungporn Wiwatanapataphee; Yong Hong Wu; Wannika Sawangtong; Panumart Sawangtong; Doungporn Wiwatanapataphee; Yong Hong Wu; Wannika Sawangtong; Panumart Sawangtong

doi:10.3934/math.2025560

AIMS Mathematics

2025, Volume 10, Issue 5: 12388-12420. doi: 10.3934/math.2025560

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Modeling anomalous diffusion and volatility in the Australian national electricity market using a space-fractional Black-Scholes framework

1.
Curtin University, School of Electrical Engineering, Computing and Mathematical Sciences, Perth, Western Australia
2.
Department of Mathematics, Faculty of Science, Mahidol University, Bangkok, Thailand
3.
Research group for fractional calculus theory and applications, Science and Technology Research Institute, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand
4.
Centre of Excellence in Mathematics, MHESI, Bangkok, 10400, Thailand
5.
Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand

Received: 21 March 2025 Revised: 14 May 2025 Accepted: 22 May 2025 Published: 27 May 2025
MSC : 26A33, 91G20

Extreme volatility, price spikes, and complex nonlinear dynamics are characteristics often shown in the electricity market, particularly the Australian national electricity market (NEM). These attributes are usually driven by supply-demand imbalances, renewable energy integration, and regulatory interventions, which make traditional pricing models, such as the Black-Scholes framework, inadequate for capturing key market behaviors like long-memory effects, heavy tails, and volatility clustering. This study developed and applied a fractional Black-Scholes model that integrated space-fractional derivatives to account for memory effects, anomalous diffusion, and extreme price movements. The proposed model was calibrated using historical NEM data, demonstrating significant improvements in the pricing of electricity options. The results suggested that it effectively captured key market behaviors. Overall, the findings offered valuable insights and provided a more accurate representation of the Australian electricity market's distinct dynamics.
- fractional Black-Scholes model,
- Australian national electricity market,
- electricity price volatility,
- volatility clustering,
- derivative pricing,
- heavy-tailed behavior
Citation: Doungporn Wiwatanapataphee, Yong Hong Wu, Wannika Sawangtong, Panumart Sawangtong. Modeling anomalous diffusion and volatility in the Australian national electricity market using a space-fractional Black-Scholes framework[J]. AIMS Mathematics, 2025, 10(5): 12388-12420. doi: 10.3934/math.2025560

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Abstract

Extreme volatility, price spikes, and complex nonlinear dynamics are characteristics often shown in the electricity market, particularly the Australian national electricity market (NEM). These attributes are usually driven by supply-demand imbalances, renewable energy integration, and regulatory interventions, which make traditional pricing models, such as the Black-Scholes framework, inadequate for capturing key market behaviors like long-memory effects, heavy tails, and volatility clustering. This study developed and applied a fractional Black-Scholes model that integrated space-fractional derivatives to account for memory effects, anomalous diffusion, and extreme price movements. The proposed model was calibrated using historical NEM data, demonstrating significant improvements in the pricing of electricity options. The results suggested that it effectively captured key market behaviors. Overall, the findings offered valuable insights and provided a more accurate representation of the Australian electricity market's distinct dynamics.

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