結構型商品之評價分析：應用最小平方蒙地卡羅模擬法

The Pricing of Structured Notes : Applying Least-Squares Monte Carlo Approach

本文研究使用蒙地卡羅模擬法，分析結構型商品的績效與增進美式選擇權定價時之精確度。Longstaff and Schwartz （2001） 最小平方蒙地卡羅模擬法廣泛應用至複雜之衍生性商品。然而，最佳之迴歸模型不易尋求，包括基底函數之種類，與基底函數次方項之選用。本論文首先將冪次多項式與最佳履約邊界值結合，成為修正後最佳履約決策。單資產結果顯示，當基底函數為二次多項式，有修正之最佳履約邊界法可減少10% RMSE。本文第二部份為個案分析，使用兩個蒙地卡羅模擬系統，以找尋認購權證之重設機率。最後個案為高受益票券（ELN），藉由改變相關係數的個數、變動幅度與不同損益方式，以分析價格變化的趨勢。

The purpose of this research is to analyze the performance of structured notes and to improve the accuracy for pricing American options via Monte Carlo simulation. The least-squares Monte Carlo approach proposed by Longstaff and Schwartz (2001) claimed to price American options with complex derivatives. However, it seems difficult to apply this approach in choosing the optimal regression settings, including different basis functions and the degree of these basis functions. This paper first combines the power polynomials with optimal exercise boundary as modified optimal exercise rule. The results in the single asset imply that the modified rule with optimal exercise boundary can decrease nearly 10% RMSE when the basis function is square degree of power polynomials. The second part of this paper is case study. In order to find the reset probability for the call warrant, the two Monte Carlo simulation systems are used in this research. For the final ELN case, we analyzed the trend of price changes when changing the number and the amplitude of correlation factors together with different payoffs.