장수 위험, 사망 위험, 거래 상대방 위험에 관한 연구
Essays on Longevity, Mortality, Counterparty Risk
- 주제(키워드) Longevity risk , Mortality risk , Counterparty risk , Stochastic mortality model
- 발행기관 아주대학교
- 지도교수 심규철
- 발행년도 2016
- 학위수여년월 2016. 2
- 학위명 박사
- 학과 및 전공 일반대학원 금융공학과
- 실제URI http://www.dcollection.net/handler/ajou/000000021479
- 본문언어 영어
- 저작권 아주대학교 논문은 저작권에 의해 보호받습니다.
초록/요약
Unexpected changes in morality rate are unavoidable economic threats for society as well as for individuals. This thesis addresses issues of fundamental importance for financial protection against longevity and mortality risks. Using the general procedure (GP), I first construct a stochastic mortality model that includes all the age-specific risk factors for forecasting mortality. Here, I use South Korean male mortality data for ages 1 to 79, from 1983 to 2010. Then, the model produced by the GP is compared with seven existing stochastic mortality models, and assessed in terms of the Bayesian Information Criterion (BIC) and mean absolute percentage error (MAPE). Based on the results, the model produced by the GP consistently outperforms other models, implying that the GP is able to extract the optimal risk factors for the projection of age-specific mortality rates. Next, I address counterparty credit risk in q/S-forward contracts between annuity providers and banks. In particular, I illustrate a framework for pricing credit valuation adjustments (CVA) for q/S-forwards using stochastic mortality models, and then examine the effectiveness of q-forwards to hedge against counterparty default risk. I ascertain that the banks can achieve the same Longevity Risk Reduction (LRR) by choosing an optimal number of q-forwards, regardless of the counterparty's credit rating. Finally, I study continuous-time optimal life insurance purchase, consumption, and portfolio management strategies for a wage earner subject to mortality risk via Markov chain approximation techniques. In this framework, financial market parameters are governed by a regime-switching process. The numerical results show the significant effect of regime switching in the optimal strategies, indicating that (1) the optimal consumption with the possibility of regime switching into a better (worse) investment opportunity state are larger (less) than those in the absence of regime switching, (2) the effect of regime switching on risky investments is negligible, and (3) the optimal insurance purchases with the possibility of regime switching into a better (worse) investment opportunity state are larger (less) than those in the absence of regime switching.
more목차
Chapter 1. Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Thesis Objectives and Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Chapter 2. Forecasting Mortality Based on the General Procedure 5
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Constructing Stochastic Mortality Model Using the General Procedure . . . . . . . . . . 6
2.2.1 The Definition of Mortality and Data Source . . . . . . . . . . . . . . . . . . . 6
2.2.2 The GP model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.3 Assessing Model Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.4 Residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.5 Properties of Mortality Indexes: Unit Root Test and Sample Cross Correlation . . 15
2.3 Modeling Time-Varying Indexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.1 Modeling GP Mortality Indexes . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.2 Modeling Cohort Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4 Evaluating Predictive Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.1 Mortality Projections for Age Range 11-79 . . . . . . . . . . . . . . . . . . . . 20
2.4.2 Mortality Projections for Age Range 1-79 . . . . . . . . . . . . . . . . . . . . . 21
2.4.3 Mortality Projections for Age Range 60-79 . . . . . . . . . . . . . . . . . . . . 24
2.5 Applications to Mortality/Longevity-linked Derivatives . . . . . . . . . . . . . . . . . . 24
2.5.1 Comparison of Mortality Fan Charts . . . . . . . . . . . . . . . . . . . . . . . 25
2.5.2 Hedging Longevity Risk using q-forwards . . . . . . . . . . . . . . . . . . . . 26
2.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Chapter 3. Counterparty Risk Valuation in q/S-Forward Derivatives and Hedge
Effectiveness 30
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2 Counterparty risk valuation for q/S-forwards . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.1 q/S-forwards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.2 Calculating CVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.3 Risk-Neutral Default Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.4 CVA Sensitivities: Delta and Gamma . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.5 Exposure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2.6 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2.7 Wrong way risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3 Risk Adjusted Exposure by Distortion Approaches . . . . . . . . . . . . . . . . . . . . 45
3.4 Hedging Effectiveness of q-forwards . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.5 Discussion and conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Chapter 4. Optimal Consumption/Investment and Life Insurance with Regime-
Switching Financial Market Parameters 51
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2 Model setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.3 Simultaneous Hamilton-Jaccobi-Bellman equations . . . . . . . . . . . . . . . . . . . . 56
4.4 Numerical Method: Markov Chain Approximation Method . . . . . . . . . . . . . . . . 57
4.4.1 Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4.2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.5 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Chapter 5. Conclusion 67
Reference
