衍生性商品與逆向抵押貸款之評價研究

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姓名

黃保憲(Pao-Hsien Huang) 查詢紙本館藏

畢業系所

財務金融學系

論文名稱

衍生性商品與逆向抵押貸款之評價研究
(Two Essays on Valuation of Derivative Contracts and Reverse Mortgages)

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摘要(中)

本文是由兩篇關於衍生性商品與逆向抵押貸款的評價研究所構成。

在第一篇研究中，針對台灣現行以房養老契約（又稱為不動產逆向抵押貸款）成效不彰的問題，本文提出評價模型用以計算公平保險費率，使政府若有意建立信用保證機制，為借款人提供信用保證時，向借款人收取保險費的評價參考。此外，本文採用市場資料進行模型參數的估計，並提供保險費率的試算結果。最後，本文呈現模型參數的敏感度分析，供信用保證機制做風險管理時使用。

在第二篇研究中，針對標的資產為自然現象(如：地震、颶風、野火…等)的多資產衍生性商品，本文在風險中立評價關係的架構下，透過多變數Gamma分配，建構一般化的多資產衍生性商品評價公式。此外，以常見的一籃子選擇權與價差選擇權做為數值範例，其數值結果顯示評價評價公式相當精確。對於無法導出評價公式的衍生性商品，本文提供多變數Gamma分配下，蒙地卡羅模擬法的評價方法，讓使用者可以尋求數值解作為評價的替代方案。

摘要(英)

This study contains two essays on valuation of derivative contracts and reverse mortgages.

In Essay 1, the pricing model for Taiwan′s reverse mortgage contract (RMC) is proposed to improve ineffective promotion. If government authorities or financial institutions try to establish a third-party credit guarantee institution, the pricing model proposed in this paper may have its reference value for the subsequent studies. Moreover, the parameter estimation methods and the numerical examinations are also provided in this article. Furthermore, this article demonstrates the sensitivity analysis for the government authorities or financial institutions to manage the risk exposure of the third-party credit guarantee institution.

In Essay 2, under the general equilibrium risk-neutral valuation relationship framework, a multi-asset pricing model based on multivariate gamma distribution is proposed to capture the features of the data of environmental phenomena. This paper demonstrates two applications to price basket options and spread options. The numerical results show that the pricing model is sufficiently accurate. As for financial instruments that do not have closed-form pricing formulas, this paper further develops the Monte Carlo simulation method to manage their pricing.

關鍵字(中)

★ 台灣以房養老契約
★ 台灣老人長期照護問題
★ 公平保險費
★ 基於消費的評價方法
★ Gamma分配族
★ 風險中立評價關係
★ 一籃子選擇權
★ 價差選擇權

關鍵字(英)

★ Taiwan’s Reverse Mortgage Contracts
★ Taiwan’s Elder Long-Term Care Problem
★ Fair Insurance Premium
★ Consumption-Based Approach
★ Gamma Distribution Family
★ Risk-Neutral Valuation Relationship
★ Basket Options
★ Spread Options

論文目次

目錄

中文摘要 i
英文摘要 ii
目錄 iii
圖目錄 vi
表目錄 vii

研究一：台灣以房養老契約設計之改良與評價 1
1. 緒論 2
2. 文獻回顧 6
3. 模型設定、市場資料、模型參數 8
3.1 利率模型 8
3.1.1 CIR 利率模型 8
3.1.2 利率資料與利率模型參數估計結果 10
3.2 房價模型 11
3.2.1 房價模型 11
3.2.2 台灣房價資料與房價模型參數估計結果 12
3.3 死亡率模型 13
3.3.1 Lee-Carter死亡率模型 13
3.3.2 台灣死亡率資料與死亡率模型參數估計結果 14
4. 台灣以房養老契約評價模型 17
4.1 台灣現行以房養老契約之評價模型 18
4.1.1 給付方式之說明 18
4.1.2 利息之說明 19
4.1.3 總貸款餘額之說明 20
4.2 台灣現行以房養老契約：加入無追索權 20
4.3 台灣現行以房養老契約：加入無追索權與利息延後支付 22
4.4 台灣現行以房養老契約：加入無追索權且終身契約 23
4.5 台灣現行以房養老契約：加入無追索權、利息延後支付且終身契約 27
4.6 評價模型之限制 28
5. 數值分析 29
6. 信用保證機制之風險分析與管理 32
6.1 房屋價值波動度的變化 32
6.2 利率的變化 33
6.3 相關係數的變化 34
6.4 存活率的變化 35
6.5 房屋維護費用率的變化 37
7. 結論 38
參考文獻 40

研究二：Pricing Multi-Assets Financial Instruments within the Consumption-Based Approach 43
1. Introduction 44
2. The MVP Model 47
2.1 Review of the Equilibrium Pricing Model 47
2.2 Multivariate Gamma Distribution Family 49
2.3 Pricing Kernel and Asset-Specific Pricing Kernel 51
2.4 The MVP Model 53
3. Applications of the MVP Model 55
3.1 Pricing General Basket Options under the MVP Model 55
3.2 The Monte Carlo Simulation Method 59
4. Numerical Examples 63
4.1 The Basket Option 63
4.2 The Spread Option 64
5. Conclusion 64
Appendix A: Pricing Kernel 65
Appendix B: Asset-Specific Pricing Kernel 66
Appendix C: The Probability Density Function of the Risky Asset Associated with the Risk Preference Parameter γ 67
Appendix D: The First Three Moments of the Underlying Basket 68
Appendix E: The Approximate Pricing Formula of the General Basket Call Options, when b=1 69
Appendix F: The Approximate Pricing Formula of the General Basket Put Options, when b=1 70
Appendix G: The Approximate Pricing Formula of the General Basket Call Options, when b=-1 71
Appendix H: The Approximate Pricing Formula of the General Basket Put Options, when b=-1 72
參考文獻 73

參考文獻

研究一：台灣以房養老契約設計之改良與評價
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研究二：Pricing Multi-Assets Financial Instruments within the Consumption-Based Approach
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指導教授

吳庭斌(Ting-Pin Wu)

審核日期

2020-4-29

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