運用關聯性結構方法及GARCH過程評價權益連結型年金內含二元選擇權

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姓名

張博閎(Po-hung Chang) 查詢紙本館藏

畢業系所

財務金融學系

論文名稱

運用關聯性結構方法及GARCH過程評價權益連結型年金內含二元選擇權
(A Copula Approach for Pricing Bivariate Options with Equity-Indexed Annuities under GARCH Process)

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摘要(中)

權益連結型年金在保險市場中被視為眾多創新產品之一，隨著商品規模與設計的快速發展，如何能評價這些複雜的商品就變成一個重要的議題。本論文主要研究雙資產連結型權益年金，對於個別資產的模擬採用風險中立NGARCH模型，並利用copula方法來模擬資產間的相關結構，並在利率隨機性下對雙資產連結型年金作訂價。本研究以S&P500和RUSSELL 2000指數做為雙資產連結標的，依據樣本期間自2000年1月至2009年12月共2500日資料觀察值，經過實證資料顯示Frank copula能較佳捕捉資產間的相關性結構，在數值分析下分別對利率為常數假設下做比較並得出結論，利率為隨機性之下EIA的價值會高於利率為常數，且在maximum及minimum設計之中模型在NGARCH下EIA價值會略高於在GARCH模型下。

摘要(英)

Equity Indexed Annuities (EIAs) are viewed as one of the most innovative products in the insurance market. With the rapid development of product design, how to evaluate these complex EIAs has becomes a very important topic. In this paper, we analyze the pricing for EIAs whose payoffs depending on two risky assets. Thus, we focus on the use of copula method to capture the dependence structure between these two assets. The asset dynamic is assumed to follow the NGARCH process. Based on the daily data of S&P500 and RUSSELL 2000 index from the period of Jan.2000 to Dec.2009, we find that Frank copula can better capture the dependence structure of the assets. In numerical analysis, we calculate the fair value of EIA products with maximum and minimum design separately. We compare the assumptions that interest rate is constant. The value of EIA products under stochastic interest rate is higher than that under a constant interest rate assumption. The EIA value will be higher when asset model is under a NGARCH process than that under a GARCH process.

關鍵字(中)

★ 關聯性結構
★ 評價權益連結型年金

關鍵字(英)

★ EIA
★ copula

論文目次

中文摘要 .......................I
ABSTRACT ...................... II
致謝辭 ........................ III
CONTENTS....................... IV
LIST OF FIGURES ............... V
LIST OF TABLE.................. VI
1. INTRODUCTION................ 1
2. LITERATURE REVIEW .......... 2
3. EIA STRUCTURE .............. 5
3.1 PRICING BIVARIATE EIA ..... 6
4. RISK NEUTRAL NGARCH MODEL... 8
4.1 STOCHASTIC INTEREST RATE MODEL .... 10
5. REVIEW OF COPULA CONCEPT ........... 11
5.1 CONDITIONAL COPULA ................ 12
5.2 COPULA-BASED AND NGARCH PROCESS ... 15
6. NUMERICAL ANALYSIS ................. 16
6.1 THE DATA .......................... 16
6.2 FIT COPULA TO DATA ................ 19
7. SENSITIVITY ANALYSIS ............... 22
8. CONCLUSION ......................... 27
APPENDIX .............................. 28
REFERENCE ............................. 29

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指導教授

楊曉文(Sharon S. Yang)

審核日期

2010-7-21

推文