在複雜的財務模型中，我們要對不同衍生性金融商品定價，使用蒙地卡羅模擬法是很重要的一個計算工具。控制變異法是普遍拿來做變異數風險減輕的一種常用方法。我們進階衍生出另一種Martingale鞅控制變異法。它適合用來處理不同的避險策略和建立避險投資組合價值的過程。實證結果發現此種Martingale控制變異法對於相對應的避險策略反映出很有效的改善和影響力。
根據這些模擬的實驗結果，我們提出一個不論市場為任何一種模型下，皆適用的避險策略，來做為實證研究分析的方法。當Delta避險策略趨近極限時，會逼近相當於一個Stop-Loss停損策略。而我們再加以調整此停損策略，使其為一強韌避險策略。此時，不論是在台灣或是美國市場，也不論是在高、中、低波動率的市場下，皆有明顯效用。尤其它在高波動率和低波動率市場中，更有顯著的改善能力。

To compute option prices under complex models, Monte Carlo simulation is an important mechanism. Martingale control variate methods are useful for variance reduction. They are suitable to cope with various hedging strategies in order to construct the value of hedging portfolio processes. As a result, the variance reduced from a martingale control variate method reflects the effectiveness of corresponding hedging strategy.
Based on these simulating experiences, we propose a model-free hedging strategy for empirical studies. As a limiting delta hedging ratio, the strategy is essentially a stop-loss strategy. Our empirical study documents that this strategy is robust under scenarios of high/middle/low volatility in Taiwan or American equity markets and it works particularly well in high and low volatility environments.

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