選擇權市場中的隱含波動率是衡量市場預期風險的重要指標。隱含柳樹法（Implied Willow Tree, IWT）作為一種具高度彈性的非參數樹狀建模方法，能夠透過反向校準市場價格，動態提取每日的隱含風險中立隨機過程，並有效改善傳統樹狀模型在刻畫尾部風險與波動率偏斜上的不足。

本研究以隱含柳樹法為核心，應用於2010年至2024年間台灣加權股價指數選擇權市場的實證資料。建構動態的樹狀結構，估計當日節點價格及未來到期期間的轉移機率，進而重建對應的隱含風險中立密度（Risk-Neutral Density, RND）。特別針對2020年COVID-19疫情期間台股劇烈震盪的極端市場環境，進行深入分析與模擬。

本研究亦比較了隱含柳樹法與傳統隱含二元樹及三元樹模型在訂價誤差與風險刻畫上的差異。結果顯示，傳統模型在選擇權訂價上誤差較大；而隱含柳樹法因具備更細緻且彈性的節點與機率調整機制，明顯降低了定價誤差並提升了尾部風險的解析度。

實證結果整體顯示，隱含柳樹法不僅具備較高的訂價準確度與風險辨識能力，也展現出良好的穩定性與適用性。然由於市場結構與資料特性差異，本研究與參考文獻之結論略有差異，提示未來應針對不同市場調整模型參數與建構方式。

綜合而言，隱含柳樹法展現出廣泛的應用潛力，不僅可用於風險管理、選擇權訂價，亦可作為投資策略設計與市場監理的有力工具，為台灣選擇權市場的理論與實務發展提供重要基礎。

Implied volatility in the options market serves as a critical indicator for measuring market risk expectations. The Implied Willow Tree (IWT) model, as a highly flexible nonparametric tree-based approach, extracts the daily implied risk-neutral stochastic process through inverse calibration of market prices, effectively improving the characterization of tail risks and volatility skewness beyond traditional tree models.

This study focuses on the application of the IWT model to empirical data from the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) options market spanning from 2010 to 2024. We construct a dynamic tree structure, estimate daily node prices and transition probabilities over different maturities, and reconstruct the corresponding risk-neutral density (RND). Special attention is given to the extreme market conditions during the COVID-19 outbreak in 2020, providing in-depth analysis and simulations.

Furthermore, this study compares the performance of the IWT model against traditional implied binomial and trinomial tree models in terms of pricing errors and risk representation. Results indicate that traditional models underperform in exhibiting larger pricing errors on options. In contrast, the IWT model’s more refined and flexible node and probability adjustment mechanisms significantly reduce pricing errors and enhance tail risk resolution.

Overall, the empirical findings demonstrate that the IWT model offers superior pricing accuracy, enhanced risk identification capabilities, and robustness. However, due to differences in market structures and data characteristics, this study is little different from our literatures conclusions, and suggesting future research should tailor model parameters and construction methods to specific markets.

In conclusion, the Implied Willow Tree model shows broad applicability, serving not only as a tool for risk management and option pricing but also for investment strategy design and market supervision, providing a valuable foundation for both theoretical and practical developments in the Taiwan options market.