本文使用 2010 至 2019 年之 S\&P500 及 費城半導體指數作為標的，以幾何布朗運動及四種 Copula 結構： Gaussian 、 Student-t 、 Clayton 、 Gumbel 進行模型配適後，以蒙地卡羅法針對配適之結果進行投資情境模擬。並且針對 10 年期及 20 年期下 GMDB 保本 、 GMMB 保證年化報酬率及 GMDB + GMMB 雙重保證三種附保證投資型商品，分析不同的資產配置策略下資產模型對風險值、準備金及期末帳戶價值的影響。

實證結果顯示 Student-t Copula 對標的資產之配適度最佳，而非一般常用的多元常態 Gaussian Copula。並且相較於其他 Copula ，以 Student-t Copula 做為模型之投資策略於後續計算之風險值及準備金較低。並且，於全期固定投資組合下，相較於考慮帳戶報酬率，選擇夏普比率較高的策略能使準備金最小。

This article use the price of S&P500 and Philadelphia Semiconductor Index from 2010-01-01 to 2019-12-31 as the target asset, and use Geometric Brownian Motion as the marginal distribution of two index with four types of copula as the joint distribution. After fitting above models, use Monte Carlo method to simulate the scenario of asset returns.

We use 10-year and 20-year GMDB, GMMB, and GMMB+GMDB product as the target and analyze the relation between investment strategy and the VaR, reserve and account value at maturity under different model.

The empirical result shows that Student-t Copula fit two stock index the most. Moreover, the investment strategy under student-t copula yield the lowest VaR and reserve compared to other copula include the common assumption of financial engineerring, Gaussian copula. On the other hand, we found that the investment strategy with higher sharpe ratio has the lowest VaR and reserve, instead of the highest annual return.

致謝 i
中文摘要 ii
Abstract iii
目錄 iv
表目錄 vi
圖目錄 vii
第一章 緒論 1
第一節 研究動機 1
第二節 研究目的 2
第三節 研究流程 2
第二章 文獻回顧 3
第一節 關聯結構 3
第二節 資產配置策略及財務模型 3
第三節 投資型商品 4
第三章 附保證投資型商品 6
第一節 商品介紹 6
第二節 監理規範 7
第四章 研究方法 9
第一節 資產模型 9
第二節 蒙地卡羅模擬法 13
第三節 商品假設及現金流、準備金計算方式 13
第四節 實驗設計 14
第五章 實證分析及結果 18
第一節 分析結果 18
第六章 結論及展望 22
第一節 結論 22
第二節 未來研究方向建議 22
附錄A 各項圖表 24
A.1 各投資組合之年化平均報酬、波動度及夏普比率 24
A.2 60 歲各投資組合下之分析指標 24
參考文獻 35

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