重設選擇權（Reset option）具有一般選擇權之特性，差別在於允許履約價格在選擇權的權利期間內可改變，如市場低迷時，標的股價下跌至相當水準致使選擇權達到深度價外，附有重設條款的買權可給予持有者一定程度的保護，使履約價格往持有者有利的方向調整，對於國內多變化的股市投資環境來說，重設選擇權的確相當具有實用性。再者重設選擇權屬於路徑相依選擇權（Path-dependent option），可根據標的資產價格在持有期間的路徑調整其履約價格，當重設條件的內容改變時，重設選擇權的價格與重設機率亦會受到影響。如何滿足投資人的投資需求卻不使商品在評價方法上過於複雜是值得去深思熟慮的。

　　本研究擬採解決PDE最有效率之ㄧ的格林函數方法，應用於解決雙重設價之重設買權評價問題。透過變數變換將Black-Scholes模型PDE簡化成線性同質熱傳導方程式（Heat equation），分析標的資產價格路徑，配合契約內容定義每一期之初始條件，並輔以遞迴積分方法轉化成一連串的初始值問題，進而解出雙重設價之重設買權價格。

　　研究結果發現積分方法應用在雙重設價之重設選擇權，不但減少了誤差，其數值收斂order可高達四，提高了計算效率。最後，針對雙重設價之重設契約中各個參數作敏感度分析。

　　Today, as the wide varieties of financial instruments dazzle, reset options trade in numerical of markets worldwide and are structured to target investor　preferences. In this article, we derive a generalization of reset call option with two predetermined dates in the case of two dependent strike resets by applying the integral representation in form of the Green's function　recursively. We solve the pricing problem of the double reset option by the recursive integral method defined as a series of initial value problems at specific discrete monitoring dates. Finally, the numerical results provide the sensitivity of reset value with respect to some variables and explore some unique characteristics of the double reset feature.

　　The findings are as follows. The proposed method exploited in our numerical example is proven to have a convergence rate of order 4. Hence, the suggested method is efficient and accurate enough to value the European double reset option. On the other hand, the discontinuities in the solutions are caused by the reset feature when pricing PDE at respective reset dates. Due to more protection toward the holders of reset options, the values of reset options are always greater than that of standard call option.

　　Moreover, there are some unique results with respect to the two strike resets and reset dates of the double reset call option:

(1)Under the same first strike reset, lower second strike resets will result in higher reset values in the cases of lower current underlying stock prices than the second strike resets and vice versa. Analogously, under the same second strike reset, lower first strike resets will result in higher reset values and give more attraction for investors in the cases of lower current underlying stock prices than the first strike resets and vice versa.

(2)As the volatility of stock returns increases, it becomes more likely that the lower reset condition will be attained so that both the strike resets can be lower to satisfy the needs of investors.

(3)Placing the reset date close to the issuing date limits its likelihood of reset. However, this principle has an exception that the reset feature is more valuable for deep out-of-the-money double reset call options when the first reset date is close to the issuing date.

(4)The reset feature has little value when the second reset date is close to the expiration date.

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