近年來，有越來越多衍生性金融商品附有重設條款，尤其是亞式重設選擇
權，亞式重設選擇權（Asian reset option）為重設選擇權的一種，可在契約期間內達重設標準後改變其履約價格，與標準重設選擇權(重設日單一收盤價)的差別在於亞式是使用重設期間的股價平均作為標的價格，而非使用重設日的單一股價作為重設的比較依據，國內目前發行的重設型認購(售)權證即屬此類。因此，若市場處於多空不明時，使用重設期間的平均價格作為依據，可避免重設日單一股價易為人為操縱的問題，此條款可使履約價與市場情況作調整，並給予持有者一定程度的保護，對於較不成熟的金融市場而言極為實用。另外，由於各個重設期間標的資產的履約價彼此會有相關性，一旦執行重設條款，會影響選擇權價格，所以重設選擇權可視為路徑相依選擇權（Path-dependent option）的一種。
本研究採用標的資產之兩日算術平均作為重設條款，即設定契約在重設期
間，選定之兩日作為算術平均重設門檻，並採用偏微分方程(Partial derivative equation)評價重設認購權證的價值。我們熱傳導方程式（Heat equation），配合契約重設條款所定義之初始條件與一系列初始質及格林函數(Green’s function)方法，透過遞迴積分方法(recursive integral method)即可得算術平均之重設買權價格。國內目前認購權證多採用兩天平均均價作為標的股價，故本研究的數值分析重設條款即以兩天算術平均均價作為重設的比較基準。研究結果發現，遞迴積分法具有精確且穩定的收斂效果，並且除了針對單點重設契約中之各個參數作敏感度分析外，亦比較算術平均與幾何平均之重設選擇權，在不同參數下，兩者的相對誤差，以證明有封閉解的幾何平均之重設選擇權可用於近似無封閉解的算術平均重設選擇權。

An Asian reset option is an option whose payoff depends on the average price of the underlying asset during some pre-specified period of time. Using the average price can not
only mitigate the possibility of stock price manipulation but also protect the investor's from downside risk. Pricing techniques up to now rely on either numerical analysis or
simulation.
This study investigates the pricing of the arithmetic average reset option. The Asian reset option is valuated, with two monitoring dates, by solving the PDE equation with the initial condition in the study. After performing the transformed Green’s function, we obtain the option value by an analytic formula through the recursive integral method. The option price is formulated as the solution of the Black-Scholes equation. In addition, the valuation is derived from a series of initial value problems based on the Green function through integration. Finally, the reset option price is numerically calculated. Moreover, throughout
the numerical method we can derive reset option prices of both arithmetic average and geometric average reset options. Numerical examples are also presented in the study for comparison.

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