本研究延伸 Teng 與 Zhou（2019）的研究，將球狀蒙地卡羅模擬法的應用範疇，從匯率連動選擇權擴展至同時涵蓋多資產、路徑相關與非路徑相關特性的結構型商品。除了使用球狀蒙地卡羅模擬法外，亦分別採用反向變數法、系統抽樣法及標準蒙地卡羅法對具自動提前出場機制之 FCN 商品進行評價。數值結果顯示，球狀蒙地卡羅雖能有效降低變異數，但在觀察日較多的情況下，必須反覆進行亂數抽樣而破壞預選單位向量集合的變異數縮減效果，導致其效率優勢不如預期；反之，若商品結構相對簡單、觀察次數僅有一天，球狀蒙地卡羅模擬法較能發揮其理論效果。

This study extends the research of Teng and Zhou (2019) by broadening the application of the spherical Monte Carlo simulation method from Quanto options to structured products featuring multiple underlying assets with both path‑dependent and path‑independent payoffs. In addition to the spherical Monte Carlo approach, we also employ antithetic variates, systematic sampling, and standard Monte Carlo methods to value a Fixed Coupon Note (FCN) .Our numerical results indicate that, although the spherical Monte Carlo method can achieve significant variance reduction, its efficiency diminishes when the number of observation dates is large—because repeated random sampling disrupts the predetermined set of unit vectors and undermines variance reduction. Conversely, when there is only a single observation date, the spherical Monte Carlo method can better demonstrate its theoretical efficiency.

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