扩展黑斯模型含随机波动率，提升期权定价精度。
Mathematical Modeling of Option Pricing with an Extended Black-Scholes Framework
- 用有限差分法求解含随机波动率的偏微分方程。
- LSTM预测更准，但有限差分法计算更快。
- 适合金融建模与量化交易研究者参考。
本研究通过在偏微分方程（PDE）框架内引入随机波动率和利率变动，对黑斯期权定价模型进行扩展。采用有限差分法求解该扩展模型，并构建了基于LSTM的机器学习模型，对谷歌股票期权进行定价评估。两种模型均使用历史市场数据进行回测。结果显示，尽管LSTM模型具有更高的预测精度，但有限差分法在计算效率上表现更优。该工作揭示了不同市场条件下模型的表现差异，强调了混合方法在稳健金融建模中的潜力。
原文摘要 · Abstract (English)
This study investigates enhancing option pricing by extending the Black-Scholes model to include stochastic volatility and interest rate variability within the Partial Differential Equation (PDE). The PDE is solved using the finite difference method. The extended Black-Scholes model and a machine learning-based LSTM model are developed and evaluated for pricing Google stock options. Both models were backtested using historical market data. While the LSTM model exhibited higher predictive accuracy, the finite difference method demonstrated superior computational efficiency. This work provides insights into model performance under varying market conditions and emphasizes the potential of hybrid approaches for robust financial modeling.
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