摘 要
随着金融市场复杂性的不断增加，传统期权定价模型在处理非线性、非对称性和市场不确定性方面逐渐暴露出局限性。为解决这一问题，本研究基于金融工程理论框架，提出了一种融合随机微积分与机器学习算法的混合期权定价模型优化方法。通过引入高斯过程回归和长短期记忆网络，构建了能够动态适应市场变化的定价机制，有效克服了传统模型中参数估计偏差大、拟合精度低的问题。实证研究表明，在沪深300股指期权市场数据测试中，该优化模型不仅显著提高了定价准确性，还将预测误差降低了25%以上。此外，模型创新性地引入了隐含波动率曲面动态调整机制，使得定价结果更贴合实际市场情况。研究还发现，相较于BSM模型和蒙特卡洛模拟法，新模型在极端市场条件下表现出更强的鲁棒性和稳定性。本研究的主要贡献在于将现代人工智能技术与经典金融理论有机结合，为复杂金融衍生品定价提供了新的思路和工具，对于完善我国资本市场定价体系具有重要理论价值和实践意义。
关键词：期权定价模型优化 随机微积分与机器学习 高斯过程回归
Abstract
With the increasing complexity of financial markets, traditional option pricing models have gradually revealed limitations in handling nonlinearity, asymmetry, and market uncertainty. To address this issue, this study proposes a hybrid option pricing model optimization method that integrates stochastic calculus with machine learning algorithms within the fr amework of financial engineering theory. By incorporating Gaussian process regression and long short-term memory networks, a pricing mechanism capable of dynamically adapting to market changes is constructed, effectively overcoming the problems of large parameter estimation bias and low fitting accuracy in traditional models. Empirical studies show that, when tested on CSI 300 index option market data, the optimized model not only significantly improves pricing accuracy but also reduces prediction errors by more than 25%. Additionally, the model innovatively introduces a dynamic adjustment mechanism for the implied volatility surface, making the pricing results more consistent with actual market conditions. The study further finds that, compared to the BSM model and Monte Carlo simulation methods, the new model demonstrates stronger robustness and stability under extreme market conditions. The primary contribution of this research lies in the organic combination of modern artificial intelligence technologies with classical financial theories, providing new approaches and tools for the pricing of complex financial derivatives, which holds significant theoretical and practical implications for improving the pricing system of China's capital markets.
Keyword:Option Pricing Model Optimization Stochastic Calculus And Machine Learning Gaussian Process Regression
目 录
引言 1
1期权定价理论基础 1
1.1经典期权定价模型回顾 1
1.2金融工程在期权定价中的应用 2
1.3现有模型的局限性分析 2
2模型优化的理论框架 3
2.1优化目标的确立 3
2.2风险中性测度的选择 3
2.3模型参数的估计方法 4
3基于随机微积分的改进 4
3.1随机过程的应用 4
3.2波动率微笑现象处理 5
3.3路径依赖型期权定价 5
4实证分析与案例研究 6
4.1数据选取与预处理 6
4.2优化模型的实证检验 6
4.3结果分析与比较研究 7
结论 7
参考文献 9
致谢 10
