系统管理学报

系统管理学报 ›› 2025, Vol. 34 ›› Issue (5): 1401-1415.DOI: 10.3969/j.issn.2097-4558.2025.05.016

• 数字经济与金融工程 • 上一篇    下一篇

基于阻尼GARCH扩散模型的碳期权定价研究

吴鑫育1，朱志田1，李心丹2   

  1. 1.安徽财经大学 金融学院，安徽 蚌埠 233030；2.南京大学 工程管理学院，南京 210008
  • 收稿日期:2024-01-25 修回日期:2024-06-09 出版日期:2025-09-28 发布日期:2025-10-16
  • 基金资助:
    国家社会科学基金重大资助项目（22ZDA112）；国家自然科学基金资助项目（71971001）；安徽省自然科学基金资助项目（2208085Y21）；安徽省高校杰出青年科研项目（2022AH020047）；安徽省高校学科（专业）拔尖人才学术资助项目（gxbjZD2022019）；安徽省高校优秀科研创新团队（2022AH010045）；安徽高校协同创新项目（GXXT-2021-078）

Carbon Option Pricing with Damped GARCH Diffusion Model

WU Xinyu1,ZHU Zhitian1,LI Xindan2   

  1. 1. School of Finance, Anhui University of Finance and Economics, Bengbu 233030, Anhui, China; 2. School of Management and Engineering, Nanjing University, Nanjing 210008, China
  • Received:2024-01-25 Revised:2024-06-09 Online:2025-09-28 Published:2025-10-16

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摘要： 本文在GARCH扩散模型中引入阻尼结构，构建了用于碳期权定价的阻尼GARCH扩散模型。该模型能够更充分地捕捉碳金融市场的波动率动态特征，尤其是在极端波动情境下的表现。通过Radon-Nikodym导数推导风险中性收益率动态性过程，并采用蒙特卡罗模拟方法计算碳期权价格。使用序贯极大似然方法，结合碳期权价格数据及其标的期货收益率数据，对定价模型参数进行估计。基于欧盟碳期权数据的实证结果表明：阻尼GARCH扩散模型在样本内和样本外定价精度上均显著优于Black模型与标准GARCH扩散模型。具体而言：样本内定价的均方根误差（RMSE）分别降低了91.03%和5.39%；样本外定价误差分别减少了86.73%和2.84%。该结论在不同评价指标下均保持稳健。进一步比较发现，阻尼GARCH扩散模型相比随机波动率跳跃（SVJ）模型在碳期权定价方面表现更优。研究结果凸显了引入阻尼扩散结构对提升碳期权定价效果的重要作用。

关键词: 碳期权定价, 阻尼GARCH扩散模型, 阻尼结构, 粒子滤波, 序贯极大似然估计

Abstract: A damped GARCH diffusion model is proposed that extends the GARCH diffusion model through the incorporation of damping structure to value carbon options. The proposed damped GARCH diffusion model has the capacity to adequately capture the volatility dynamics, particularly the extreme volatility in the carbon financial market. The risk-neutral return dynamic is derived relying on the Radon-Nikodym derivative. Using the Monte Carlo simulation method, the prices for carbon options are computed. A sequential maximum likelihood method is developed to estimate the parameters of the pricing model using data on the carbon option prices and underlying asset (carbon futures) returns. An empirical analysis based on EUA options shows that damped GARCH diffusion model outperforms the Black and GARCH diffusion models in both in-sample and out-of-sample option pricing. To be specific, the root-mean-square error (RMSE) for the damped GARCH diffusion model is 91.03% and 5.39% lower than that of the Black and GARCH diffusion models in in-sample option pricing, while it is 86.73% and 2.84% in out-of-sample option pricing. The findings are robust to different evaluation criteria. Further discussion demonstrates that the damped GARCH diffusion model outperforms the stochastic volatility jump (SVJ) model in carbon option pricing. The findings highlight the critical importance of incorporating damped diffusion structure in carbon option pricing.

Key words: carbon option pricing, damped GARCH diffusion model, damping structure, particle filter, sequential maximum likelihood estimation

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