Two Essays on the Application of Contingent Approach: The Case of No-Negative-Equity-Guarantees and Weather Derivative

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姓名

黃志偉(Jr-Wei Huang) 查詢紙本館藏

畢業系所

財務金融學系

論文名稱

(Two Essays on the Application of Contingent Approach: The Case of No-Negative-Equity-Guarantees and Weather Derivative)

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摘要(中)

本論文藉由衍生性商品評價方法與應用來探討長壽風險與氣候風險之議題，其一為不為負權益保證之評價，另一為氣候衍生性商品之評價。
　　第一篇文章為探討英國不為負權益保證之評價方法與實證分析。為反應其商品所有之風險特性，本文在評價不為負權益保證時考量了房價報酬、利率及死亡率具有隨機之特性外並進一步考慮房價具有跳躍的現象。在實證分析上，我們發現英國房價報酬具有顯著跳躍、自我相關及波動叢聚之特性，故在房價模型本文延用Chan and Maheu (2002)所提出 Jump ARMA-GARCH 模型。在利率與死亡率隨機性方面，本文分別採用CIR模型(Cox et al.,1985)與CBD模型(Cairns et al.,2006)進行分析與模擬。最後，本文利用Bühlmann et al. (1996)所提出Conditional Esscher Transform進行不為負權益保證的理論評價，進而提供合理的商品價格。由數值分析結果發現，房價之跳躍現象，利率風險及死亡率風險等均會影響英國不為負權益保證價格，其中以利率風險影響最鉅。在模型風險方面，本文針對不同的房價模型進行分析比較如Black　Scholes, Merton Jump, ARMA-GARCH, ARMA-EGARCH, Double Exponential Jump Diffusion, Jump ARMA-GARCH模型。
　　第二章文章為氣候衍生性商品之評價方法與實證分析。氣候影響著我們每日的生活及選擇並對全球經濟活動造成巨大的影響。因此，如何規避氣候風險便成為一個相當重要的課題。近年來，店頭市場與集中市場已成功推出許多氣候衍生商品來規避不利的氣候因素所造成的經濟損失，然而在眾多的氣候衍生商品中，最常被交易的標的資產為氣溫。透過觀察台灣每日日均溫之動態行為，本文進一步提出ARFIMA-SGARCH模型捕捉台灣每日日均溫之動態過程。其實證結果發現，ARFIMA-SGARCH在溫度的配適及預測能力皆比傳統溫度模型來的出色。最後，本文進一步利用Cao and Wei(2004)所提出定價模型對氣候衍生性商品進行評價。

摘要(英)

This dissertation contains two essays on the valuations of derivative approach to further explore longevity risk and weather risk issue. One is valuing No-Negative-Equity-Guarantee (NNEG) and another is valuation of weather derivative.
First Essay:
Pricing No-Negative-Equity Guarantees for Equity Release Products
To reflect the risks involving with equity releasing products, this study considers stochastic house price returns, interest rates and mortality rates to price no-negative-equity guarantees (NNEG). Particularly, we investigate the jump effect with house price returns. Observing from the data of U.K. house returns with significant persistence jumps, autocorrelation and volatility clustering, we propose a jump ARMA-GARCH model. Assuming the interest rate dynamics follow the CIR model (Cox et al.,1985) and mortality rate dynamics based on CBD model(Cairns et al.,2006), we derive a risk neutral valuation framework for NNEG using the conditional Esscher transform technique developed by Bühlmann et al. (1996). The numerical analysis reveals that the jump effect with house price returns, interest rate risk and mortality rate risk can affect the cost of NNEG and the impact is as significant as that for interest rate risk. Moreover, we demonstrate the model risk on pricing NNEG by comparing various house price return models of Black-Scholes, Merton Jump, ARMA-GARCH, ARMA-EGARCH, Double Exponential Jump Diffusion, Jump ARMA-GARCH models.
Second Essay:
Long Memory in Temperature: Detection, Modeling, and Valuation the Weather Derivatives
Weather influences our daily lives and choices and has an enormous impact on economy activity. The hedging of weather risks has become extremely relevant in recent years, promoting the diffusion of weather derivative contracts. The valuation of such contracts require the development of appropriate model for the prediction of underlying weather variable. Within this framework, we propose the ARFIMA- SGARCH model in order to model the daily average temperature dynamic evolution, as we observed the temperature process. Our model show a significant improvement fitting and forecasting performance compare with traditional temperature model. Finally, we present an application related to the forecast and simulation of temperatures indices used for the valuation of weather derivative proposed by Cao and Wei (2004).

關鍵字(中)

★ 不為負權益保證
★ 跳躍風險
★ 利率風險
★ 死亡率風險
★ 氣候衍生性商品
★ 氣溫
★ 長記憶

關鍵字(英)

★ No-Negative-Equity Guarantees
★ Jump Risk
★ Interest Rate Risk
★ Mortality Rate Risk
★ Weather Derivative
★ Temperature
★ Long Memory

論文目次

Contents
Chinese Abstract i
English Abstract iii
Contents v
List of Figures vii
List of Tables viii
First Essay Pricing No-Negative-Equity Guarantees for Equity Release Products
1. Introduction 1
2. Investigation of House Price Returns with Jumps 6
2.1 The Jump ARMA(s,m)-GARCH(p,q) 6
2.2 Empirical Analysis of Model Fit 9
3. Valuation of No-Negative-Equity Guarantee under House Price Return, Interest Rate, and Mortality Rate Dynamics 12
3.1 The Payoff of NNEG 12
3.2 The Valuation Framework of NNEG 13
3.3 Risk-Neutral Valuation 15
3.3.1 Housing Price Model 15
3.3.2 Interest Rate Model 17
3.3.3 Mortality Model 18
4. Cost of No-Negative-Equity Guarantee 19
4.1 The Effect of Jump risk of House Price Returns 19
4.2 The Effect of Mortality Risk 20
4.3 The Effect of Interest Rate Risk 21
4.3 The Three Factors Risks Effect on NNEG 21
5. Conclusion 22
Reference 24
Appendix A: Investigation of ARMA(s,m)-GARCH(p,q) Model 28
Appendix B 30
Appendix C 33
Appendix D 35
Appendix E 36
Second Essay Long Memory in Temperature: Detection, Modeling and Valuation the Weather Derivative.
1. Introduction 51
2. Detecting Long Memory with Temperature Data in Taiwan 56
2.1 Statistical Analysis of Temperature Data 56
2.2 Application the Long Memory Test for Temperature 57
2.2.1 Hurst (1951) 58
2.2.2 Lo (1991) 59
2.2.3 Geweke and Porter-Hudak (1983) 60
3. Modeling Taiwan Average Temperature Time Series 61
3.1 Dynamic Modeling of the Temperature Process Using ARFIMA - SGARCH Model 62
3.2 A Comparison of ARFIMA-SGARCH Model 63
3.3 Empirical Comparison of Forecasts of the Daily Average Temperature 67
4. Valuation Framework under ARFIMA-SGARCH Model 69
4.1 Valuation of HDD/CDD Derivatives 71
4.2 Market Price of Risk 72
4.3 The Results of Simulation 72
5. Conclusion 74
Reference 76

List of Figures
First Essay Pricing No-Negative-Equity Guarantees for Equity Release Products
Figure 1 Historical Returns of U.K. Nationwide House Price Index 41
Figure A.1 Sample ACF of the Log-Return on the U.K. House Price Index 41
Figure A.2 U.K. Volatility Changes Over Time 42
Figure A.3 Sample ACF of the Residuals of the Best Fit ARMA Model 42
Figure A.4 Sample ACF of the Squared Residuals of the Best Fit ARMA Model 43
Figure D.1 Estimated Values of and for Men (Top) and Women (Bottom) 43
Second Essay Long Memory in Temperature: Detection, Modeling and Valuation the Weather Derivative.
Figure 1 The Figure Displays a Time Series Plot of Daily Average Temperature, 1970-2011 79
Figure 2 Histograms and Descriptive Statistic for Daily Average Temperature 79
Figure 3 Standard Deviation of Date Temperautre 80
Figure 4 The Figure show observed ACF for Taiwan Temperature. The Gray Area show the 95% confidence intervals around the observed estimate 80

List of Tables
First Essay Pricing No-Negative-Equity Guarantees for Equity Release Products
Table 1 Summary Statistics, 1953Q4–2008Q4 44
Table 2 Estimates and Model Fit of the Constant and Dynamic Jump ARMA(3,2) GARCH(1,1) Models for 1953Q4–2008Q4 45
Table 3 Model Selection, 1953Q4–2008Q4 46
Table 4 Model Selection, 1958Q4–2008Q4 46
Table 5 Model Selection, 1968Q4–2008Q4 47
Table 6 Base Assumption of Parameter Values for Pricing NNEG 47
Table 7 The Cost of NNEG under Various House Price Return Models 48
Table 8 The Effect of Mortality Risk on the Cost of NNEG 49
Table 9 Impact of Jump Effect on the Cost of NNEG with Stochastic Interest Rate 49
Table 10 Impact of Risks Effect on the Cost of NNEG 50
Table A.1 BIC for an ARMA(s,m) 50
Second Essay Long Memory in Temperature: Detection, Modeling and Valuation the Weather Derivative.
Table 1 The Unit Root Test and Long Memory Test for Daily Average Temperature from 1970/01/01 to 2011/12/31 81
Table 2 Parameter Estimated for Daily Average Temperature from 1970/01/01 to 2011/12/31 82
Table 3 Temperature Models Comparison 83
Table 4 Model Selection, 01/01/1970-31/12/2011 83
Table 5 Model Selection, 01/01/1970-31/12/2010 84
Table 6 Forecasting Error for Different Models, 01/01/2011-31/12/2011 84
Table 7 Fitting and Forecasting Error Improve for Different Models 85
Table 8 Base Assumption of Parameter Values for Pricing Weather Derivative 85
Table 9 Risk Premium in Forward Prices: Lagged Correlations 86
Table 10 Risk Premium in Call Prices: Lagged Correlations 87
Table 11 Risk Premium in Put Prices: Lagged Correlations 88
Table 12 Impact of Mean Reversion in the Dividend Process 89

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指導教授

張傳章、楊曉文
(Chuang-Chang Chang、Sharon S. Yang)

審核日期

2013-7-3

推文