本論文將物理資訊神經網路（Physics-Informed Neural Networks， PINNs）應用於雙因子 Hull–White 模型（等價於 G2++ 模型）下之零息債券定價，該模型相較於單因子模型，在捕捉實證利率期限結構動態上具有更大的彈性。為求解風險中性測度下的債券定價偏微分方程，神經網路架構將到期支付條件直接嵌入輸出層，而非以軟懲罰項的方式加入損失函數，從而確保邊界條件的精確滿足並提升訓練穩定性。為對框架進行實證驗證，模型參數由美國隔夜銀行資金利率及公債殖利率日資料（2016 年 3 月至 2025 年 2 月）估計而得，採用結合普通最小平方迴歸與 Nelson–Siegel 殖利率曲線擬合的兩階段估計程序。基於上述估計參數，經校準之 PINN 框架分別於樣本內及樣本外滾動測試中進行評估，在所有到期期限上均達到顯著低於解析解基準的定價誤差。上述結果顯示，物理資訊神經網路在市場一致性零息債券定價上具有實際應用潛力。;This study develops a Physics-Informed Neural Network (PINN) framework for zero-coupon bond pricing under the Two-Factor Hull-White model (equivalently， the G2++ model)， which offers greater flexibility in capturing empirical term-structure dynamics than single-factor models. To solve the governing bond-pricing PDE under the risk-neutral measure， the neural network architecture encodes the terminal payoff condition directly into its output layer rather than as a soft penalty term， guaranteeing exact boundary satisfaction and improving training stability. To empirically validate the framework， model parameters are estimated from daily U.S. Overnight Bank Funding Rate and Treasury yield data spanning March 2016 to February 2025， using a two-step procedure combining Ordinary Least Squares regression and Nelson–Siegel yield curve fitting. Using these estimated parameters， the calibrated PINN framework is evaluated in both in-sample and out-of-sample rolling tests， achieving substantially lower pricing errors than the analytical benchmark across all maturities. These findings suggest that Physics-Informed Neural Networks hold practical potential for market-consistent zero-coupon bond pricing.
