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研究生： 徐振傑
HSU, CHEN-CHIEH
論文名稱： 基於多模態物理資訊與圖形注意力之選擇權定價與避險框架
A Multimodal Physics-Informed and Graph Attention Framework for Option Pricing and Hedging
指導教授： 鄭憲宗
Cheng, Sheng-Tzong
學位類別： 碩士
Master
系所名稱： 工學院 - 智慧製造國際碩士學位學程
International Master Program on Intelligent Manufacturing
論文出版年： 2026
畢業學年度： 114
語文別： 英文
論文頁數： 84
中文關鍵詞： 選擇權定價 、長短期記憶網路 、圖注意力網路 、物理資訊神經網路 、Greeks
外文關鍵詞： option pricing, long short-term memory, graph attention network, physics-informed neural network, Greeks
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    • 選擇權定價同時涉及標的資產動態、契約橫截面結構與風險敏感度估計，為衍生性金融商品研究中的重要議題。傳統 Black-Scholes 模型雖具理論基礎，然其建立於常數波動率等理想化假設之上，難以充分反映真實市場中之波動率微笑、報價噪音與不同契約間的交互影響。近年來，深度學習方法因具備優異之非線性建模能力，逐漸被應用於金融定價問題；然而，若僅使用單一時序模型，仍可能忽略跨契約資訊、缺乏基本金融結構約束，並導致 Greeks 學習不穩定。基於此，本研究以 SPY 選擇權日資料為對象，建構一套分階段深度學習定價框架，依序比較 Baseline LSTM、GAT-LSTM、PI-GAT-LSTM 與 Sobolev PI-GAT-LSTM 四類模型。於資料處理階段，先對原始選擇權報價進行品質過濾，排除異常 bid-ask 組合、過大價差、過低中間價與極端到期樣本，並建構包含 moneyness、到期時間、forward moneyness、隱含波動率、成交量、流動性與市場 Greeks 等特徵。其後，採用固定時間切分與 purge gap 建立訓練、驗證及測試資料集，以降低時間序列資訊洩漏風險。實驗結果顯示，隨著模型逐步引入橫截面關聯、軟式無套利約束與 Greeks 聯合監督，定價表現與曲面穩定性均獲得改善，顯示結合金融結構資訊之深度學習方法，對選擇權定價研究具有良好之應用潛力。

    Option pricing is a central problem in quantitative finance, as it simultaneously involves underlying asset dynamics, cross-sectional contract structure, and the estimation of risk sensitivities. Although the Black-Scholes model provides a rigorous theoretical foundation, its underlying assumptions, such as constant volatility, are often too restrictive to fully capture volatility smiles, market quotation noise, and inter-contract interactions observed in real markets. In recent years, deep learning methods have been increasingly applied to financial pricing problems due to their strong nonlinear modeling capability. However, a single sequence model may still overlook cross-contract information, lack fundamental financial structure constraints, and produce unstable Greek estimates. To address these issues, this study develops a stage-wise deep learning framework for SPY option pricing and compares four model variants: Baseline LSTM, GAT-LSTM, PI-GAT-LSTM, and Sobolev PI-GAT-LSTM. In the data preprocessing stage, raw option quotes are first filtered to remove abnormal bid-ask pairs, excessively wide spreads, extremely low mid prices, and contracts with extreme maturities. A set of features is then constructed, including moneyness, time to maturity, forward moneyness, implied volatility, trading volume, liquidity, and market Greeks. The dataset is subsequently divided into training, validation, and testing subsets using a fixed chronological split with a purge gap to reduce the risk of temporal information leakage. The empirical results show that, as the framework progressively incorporates cross-sectional dependencies, soft no-arbitrage constraints, and joint Greek supervision, both pricing performance and surface stability improve. These findings suggest that deep learning methods augmented with financial structural information offer strong potential for option pricing applications.

    摘要 ii Abstract iii ACKNOWLEDGMENT v TABLE OF CONTENTS vi LIST OF FIGURES viii LIST OF TABLES ix Chapter 1. Introduction & Motivation 1 Chapter 2. Background & Related Work 6 2.1 Classical Option Pricing Theory and Empirical Stylized Facts 6 2.2 Neural Network-Based Option Pricing 7 2.2.1 Comparison Between Early Neural Networks and Traditional Models 7 2.2.2 Application of Deep Learning Architectures in Option Pricing 8 2.2.3 The Role of LSTM and GRU in Volatility and Option Pricing 8 2.3 Application of Graph Neural Networks and Attention Mechanisms in Financial Markets 9 2.3.1 Graph Neural Networks and Momentum Spillover Effects 9 2.3.2 Attention Mechanisms in Financial Time Series and Volatility Surface Prediction 10 2.4 Physics-Informed Neural Networks and Arbitrage-Free Option Pricing 11 2.5 Differential Machine Learning and Sobolev Training 12 2.5.1 Differential Machine Learning: Joint Learning of Prices and Sensitivities 12 2.5.2 Sobolev Training and Function Derivative Supervision 13 2.6 Research Innovation and Thesis Positioning 14 Chapter 3. Methodology 17 3.1 Notation and Symbols 18 3.2 Problem Definition and Overall Research Framework 19 3.3 Market Settings and Data Structure 21 3.4 Baseline: Pure LSTM Pricing Model 25 3.5 Stage 1：GAT-LSTM and Temporal Self-Attention 27 3.6 Stage 2: PI-GAT-LSTM and Black-Scholes PDE Constraints 30 3.7 Stage 3: Sobolev PI-GAT-LSTM and Differential Machine Learning 34 3.8 Experimental Design and Ablation Strategy 37 Chapter 4. Implementation & Experiments 39 4.1 Implementation Framework and Experimental Design 39 4.2 Evaluation Metrics and Ablation Study Settings 45 4.3 Overall Experimental Results 47 4.4 In-depth Analysis of Evaluation Metrics 52 4.4.1 MAE Analysis 52 4.4.2 RMSE Analysis 52 4.4.3 MAPE Analysis 53 4.4.4 R2 Analysis 53 4.5 Bucket Analysis Results 54 4.5.1 Moneyness Analysis for CALL Options 57 4.5.2 Time to Maturity Analysis for CALL Options 57 4.5.3 Moneyness Analysis for PUT Options 57 4.5.4 Time to Maturity Analysis for PUT Options 58 4.6 Analysis of Training Process and Convergence Behavior 58 4.7 Comprehensive Multi-Metric Comparison and Robustness Analysis 60 4.8 Financial Implications of Sobolev Derivative Supervision 63 Chapter 5. Conclusion & Future Work 65 5.1 Research Conclusions 65 5.2 Future Work 68 Reference 71

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