本研究在不考慮死亡率的假設下，探討收取比例費用及固定費用的最低提領保證變額年金（Guaranteed Minimum Withdrawal Benefit, GMWB）之定價及動態避險之方法，並以例子來觀察動態避險在模擬資料中損益現值的分佈，及歷史資料的動態避險結果。
GMWB 的定價，與每期保險公司所收之費用及被保險人提領的金額有關，不易推導定價公式。因此我們假設已知被保險人未來提領情境，並以風險中立評價模型、 GMWB 保險商品模型及蒙地卡羅模擬法，在 Q-measure 下進行定價。
避險則以市場上可購買，且與投資標的相關性高的避險資產，進行動態避險策略的建構。本研究使用正交廣義自回歸條件異方差模型（Orthogonal Generalized Auto Regressive Conditional Heteroskedasticity, O-GARCH）來估計避險資產及 GMWB 價值的共同分佈，計算各個避險資產最佳化避險比例，最小化 GMWB 價值變化的變異數。在最後與傳統上常用的 Delta 避險與不避險的情境進行比較，觀察在 P-measure 情境下，保險公司在避險前後損益現值分佈的差別。

This paper investigates in valuation and hedging of Guaranteed Minimum Withdrawal Benefit (GMWB) variable annuity, and demonstrating the results of dynamic optimal hedging on simulated data and historical data.
The value of GMWB is related to fees and withdrawals, and it is hard to be valued with formula. Therefore, given the withdrawal schedule, we can value GMWB with the risk-neutral valuation method and the Monte Carlo method in Q-measure.
The goal of dynamic optimal hedging strategy is to minimize volatility of hedging errors. We choose hedging assets with high return correlation with the underlying asset and computing optimal hedging ratios of hedging assets with the joint probability distribution of assets to minimize the volatility of hedging errors. The joint probability distribution can be derived from the orthogonal generalized autoregressive conditional heteroskedasticity model (O-GARCH). At the end of this paper, we compare optimal hedging with delta hedging and un-hedging, concluding the hedging performance of optimal hedging.

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