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。所以，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。
本研究採用一般化的重設條款，即可設定契約有多層重設期間，且每一期間內使用多個觀察日的平均價，並採用偏微分方程(Partial derivative equation)評價重設認購權證的價值。我們透過變數變換可將Black-Scholes的PDE簡化成熱傳導方程式（Heat equation），配合契約重設條款所定義之初始條件及格林函數(Green’s function)方法，透過遞迴積分方法(recursive integral method)即可解亞式重設買權價格。
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幾何平均均價作為重設的比較基準。研究結果發現，遞迴積分法具有一定的收斂效果，並且除了針對單點與雙點之重設契約中之各個參數作敏感度分析外，亦比較亞式與標準型(單日股價)的重設條款不同，對選擇權價值之影響。

On the Taiwanese financial market, most reset warrants belong to Asian reset option, which will reset its exercise price as the pre-specified reset strike, if the geometric average underlying price, not single closing price, falls on the reset criteria at the pre-determined monitoring window. Using multi-day average price can prevent the manipulated possibility of the stock prices and lessen the question of a delta jump resulting in the difficulty of risk management. In addition, it is also a path-dependent derivative whose payoff is based on the historical average stock prices.
This research valuates the Asian reset option with multiple monitoring windows by solving the PDE equation with the initial condition. After performing the Heat Equation transformed into the Black-Scholes PDE, we solve the Heat Equation solve the Heat Equation through the Green’s function and the boundary element method and then obtain the option value by an analytic formula through the recursive integral method.
In our numerical results, we take a contract with two-day geometric average underlying price as the comparison with the dependent strike resets and one or two reset windows. We find the integral representation will be convergent as increasing the number of intervals based on a quadratic polynomial approximation. Furthermore, we make some sensitivity analysis for the general parameters and unique factors of reset clauses. Compare the option value using two-day average as base with a standard reset contract (single closing price), we illustrate how the value difference makes the effect on the current underlying prices.

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