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題名 財務風險管理與清償能力機制之研究分析
Essays on Financial Risk Management and Solvency Assessment Mechanisms
作者 杜昌燁
Tu, Chang-Ye
貢獻者 張士傑
杜昌燁
Tu, Chang-Ye
關鍵詞 界限選擇權
百慕達式選擇權
有限元素法
李群分析
國際板債券
再投資風險
Barrier options
Bermudan options
Finite element methods
Lie group analysis
International bonds
Reinvestment risks
日期 2021
上傳時間 4-Aug-2021 14:52:59 (UTC+8)
摘要 本研究由四篇關於金融風險管理和償付能力評估議題的論文所構成，這些論文充分使用了界限與百慕達式選擇權的分析概念。本文第二章針對早期預警系統下的各種情境計算被保險人的終端期望效用，協助保險公司進行資產負債管理決策。早期預警系統的建構由指定破產與監理邊界開始，當資產價值觸及監理邊界時進行一系列的處置，如改變投資組合與增資等。在本文資產模型下的計算顯示，當資產降至監理邊界之低水平時，改變投資組合與增資並行可使終端期望效用最大化；以上的計算過程使用了與評價界限選擇權相同的複雜違約概率表示式。第三章介紹有限元素法理論，同時應用在雙界限選擇權定價問題。數值計算結果驗證有限元素法求解選擇權問題的準確性。在第四章中，李群分析技術被用於建構源自 Merton 最適消費投資問題的 Hamilton-Jacobi-Bellman (HJB) 方程式的精確解，而此精確解指出了 Merton 對最適消費投資問題處理之不足處。第五章討論國際板債券的再投資風險，並與所有贖回情境下的最大預期損失相連結。再投資風險的估計等同於百慕達式選擇權的評價；歷史資料統計指出國際板債券的收益率隨機模型遵循指數 Lévy 過程，因此可使用 COS 法等高效數值方法進行評價。在當前市場條件下，國際板債券的再投資風險估計為 113 至 189 bps，具體取決於初始宣告收益率。
The thesis is a collection of four papers on topics of financial risk management and solvency assessment which exploit the concept and the analytics of barrier and Bermudan options. In chapter 2, the terminal expected utility of the insured under the early warning system are computed for different regulatory schemes, and the results provide the insight for the insurer`s asset-liability management decisions. The explicit consideration of the early warning system involves intricate default probability expressions of the underlying asset model, which is the essential ingredient for pricing barrier options. Chapter 3 introduces one of the most accurate numerical methods, namely the finite element method (FEM). The remarkable accuracy is demonstrated by applications to the pricing of double barrier options. In chapter 4, the Lie group analysis techniques is applied to construct the exact solution of the Hamilton-Jacobi-Bellman (HJB) equation arising in the classical optimal consumption-investment problem solved by Merton. The upshot of the analysis is that Merton`s treatment of the problem is incomplete and more emphasis should be placed on the bankruptcy scenario. In chapter 5, it is argued that the reinvestment risk of the international bonds is associated with the maximum expected loss in all redemption scenarios, and the underlying stochastic internal rate of return model of international bonds follows the exponential Lévy process. The evaluation of the reinvestment risk is equivalent to the pricing of a certain non-standard Bermudan option and efficient numerical method such as the COS method can be applied. Under current market condition the reinvestment risk is estimated to be 113 to 189 bps, depending on the initial IRR.
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描述 博士
國立政治大學
風險管理與保險學系
105358502
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0105358502
資料類型 thesis
dc.contributor.advisor 張士傑zh_TW
dc.contributor.author (Authors) 杜昌燁zh_TW
dc.contributor.author (Authors) Tu, Chang-Yeen_US
dc.creator (作者) 杜昌燁zh_TW
dc.creator (作者) Tu, Chang-Yeen_US
dc.date (日期) 2021en_US
dc.date.accessioned 4-Aug-2021 14:52:59 (UTC+8)-
dc.date.available 4-Aug-2021 14:52:59 (UTC+8)-
dc.date.issued (上傳時間) 4-Aug-2021 14:52:59 (UTC+8)-
dc.identifier (Other Identifiers) G0105358502en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/136368-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 風險管理與保險學系zh_TW
dc.description (描述) 105358502zh_TW
dc.description.abstract (摘要) 本研究由四篇關於金融風險管理和償付能力評估議題的論文所構成，這些論文充分使用了界限與百慕達式選擇權的分析概念。本文第二章針對早期預警系統下的各種情境計算被保險人的終端期望效用，協助保險公司進行資產負債管理決策。早期預警系統的建構由指定破產與監理邊界開始，當資產價值觸及監理邊界時進行一系列的處置，如改變投資組合與增資等。在本文資產模型下的計算顯示，當資產降至監理邊界之低水平時，改變投資組合與增資並行可使終端期望效用最大化；以上的計算過程使用了與評價界限選擇權相同的複雜違約概率表示式。第三章介紹有限元素法理論，同時應用在雙界限選擇權定價問題。數值計算結果驗證有限元素法求解選擇權問題的準確性。在第四章中，李群分析技術被用於建構源自 Merton 最適消費投資問題的 Hamilton-Jacobi-Bellman (HJB) 方程式的精確解，而此精確解指出了 Merton 對最適消費投資問題處理之不足處。第五章討論國際板債券的再投資風險，並與所有贖回情境下的最大預期損失相連結。再投資風險的估計等同於百慕達式選擇權的評價；歷史資料統計指出國際板債券的收益率隨機模型遵循指數 Lévy 過程，因此可使用 COS 法等高效數值方法進行評價。在當前市場條件下，國際板債券的再投資風險估計為 113 至 189 bps，具體取決於初始宣告收益率。zh_TW
dc.description.abstract (摘要) The thesis is a collection of four papers on topics of financial risk management and solvency assessment which exploit the concept and the analytics of barrier and Bermudan options. In chapter 2, the terminal expected utility of the insured under the early warning system are computed for different regulatory schemes, and the results provide the insight for the insurer`s asset-liability management decisions. The explicit consideration of the early warning system involves intricate default probability expressions of the underlying asset model, which is the essential ingredient for pricing barrier options. Chapter 3 introduces one of the most accurate numerical methods, namely the finite element method (FEM). The remarkable accuracy is demonstrated by applications to the pricing of double barrier options. In chapter 4, the Lie group analysis techniques is applied to construct the exact solution of the Hamilton-Jacobi-Bellman (HJB) equation arising in the classical optimal consumption-investment problem solved by Merton. The upshot of the analysis is that Merton`s treatment of the problem is incomplete and more emphasis should be placed on the bankruptcy scenario. In chapter 5, it is argued that the reinvestment risk of the international bonds is associated with the maximum expected loss in all redemption scenarios, and the underlying stochastic internal rate of return model of international bonds follows the exponential Lévy process. The evaluation of the reinvestment risk is equivalent to the pricing of a certain non-standard Bermudan option and efficient numerical method such as the COS method can be applied. Under current market condition the reinvestment risk is estimated to be 113 to 189 bps, depending on the initial IRR.en_US
dc.description.tableofcontents 中文摘要 i
Abstract ii
Contents iii
List of Tables v
List of Figures vii

1 Introduction and Outline 1

2 Optimal Insurance Solvency Regulatory Schemes Under the Early Warning System 3
2.1 Introduction 3
2.2 The Model Setup 4
2.3 Theoretical Tools 11
2.4 Numerical Results 16
2.5 Conclusions 21
2.6 Proof of (2.3.2) and (2.3.3) 21

3 Finite Element Methods in Pricing of Barrier Options 25
3.1 Introduction 25
3.2 Mathematical Prerequisites 28
3.3 The Finite Element Method 37
3.4 Pricing of Barrier Options 46
3.4.1 The Black-Scholes Model 47
3.4.2 Heston Stochastic Volatility Model 52
3.4.3 Analytical Solutions 56
3.4.4 Numerical Solutions by Finite Element Methods 58
3.5 Conclusions 63

4 Note on Merton’s Optimal Consumption-Investment Problem 64
4.1 Introduction 64
4.2 The Optimal Consumption-Investment Problem 66
4.3 Rudiments of Lie Group Analysis 68
4.4 Symmetry Group Admitted by Merton’s Equation 76
4.5 Invariant Solution of Merton’s Equation 80
4.6 Discussion and Conclusions 83

5 Estimation of Reinvestment Risk of International Bonds 84
5.1 Introduction 84
5.2 Reinvestment Risk of Callable Zero-Coupon Bonds 86
5.3 The Stochastic Internal Rate of Return Model Based on Exponential Lévy Processes 88
5.4 Stochastic Internal Rate of Return Model Selection and Parameter Estimation 90
5.5 Computation of Reinvestment Risk: The COS Method 93
5.6 Numerical Results 98
5.7 Conclusions 99

Appendix A Optimal Insurance Solvency Regulatory Schemes Under the Early Warning System: Code 103

Appendix B Finite Element Methods in Option Pricing: Code 117

Appendix C Estimation of Reinvestment Risk of International Bonds: Code 124

Bibliography 129		zh_TW
dc.format.extent 2075290 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0105358502en_US
dc.subject (關鍵詞) 界限選擇權zh_TW
dc.subject (關鍵詞) 百慕達式選擇權zh_TW
dc.subject (關鍵詞) 有限元素法zh_TW
dc.subject (關鍵詞) 李群分析zh_TW
dc.subject (關鍵詞) 國際板債券zh_TW
dc.subject (關鍵詞) 再投資風險zh_TW
dc.subject (關鍵詞) Barrier optionsen_US
dc.subject (關鍵詞) Bermudan optionsen_US
dc.subject (關鍵詞) Finite element methodsen_US
dc.subject (關鍵詞) Lie group analysisen_US
dc.subject (關鍵詞) International bondsen_US
dc.subject (關鍵詞) Reinvestment risksen_US
dc.title (題名) 財務風險管理與清償能力機制之研究分析zh_TW
dc.title (題名) Essays on Financial Risk Management and Solvency Assessment Mechanismsen_US
dc.type (資料類型) thesisen_US
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dc.identifier.doi (DOI) 10.6814/NCCU202101000en_US