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| 研究生： |
莊明哲 Chuang, Ming Che |
|---|---|
| 論文名稱： |
跳躍風險與隨機波動度下溫度衍生性商品之評價 Pricing Temperature Derivatives under Jump Risks and Stochastic Volatility |
| 指導教授： |
林士貴
Lin, Shih Kuei |
| 學位類別： |
博士
Doctor |
| 系所名稱： |
商學院 - 金融學系 Department of Money and Banking |
| 論文出版年： | 2015 |
| 畢業學年度： | 103 |
| 語文別： | 英文 |
| 論文頁數： | 125 |
| 中文關鍵詞： | 日均溫 、冷氣指數／暖氣指數衍生性商品 、風險中立評價法 、隨機波動度 、跳躍風險 、粒子濾波演算法 、期望最大演算法 |
| 外文關鍵詞： | daily average temperature index, CDD/HDD derivatives, risk-neutral pricing method, stochastic volatility, jump risk, particle filter algorithm, expectation-maximization algorithm |
| 相關次數： | 點閱：88 下載：6 |
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本研究利用美國芝加哥商品交易所針對 18 個城市發行之冷氣指數／暖氣指數衍生性商品與相對應之日均溫進行分析與評價。研究成果與貢獻如下：一、延伸 Alaton, Djehince, and Stillberg (2002) 模型，引入跳躍風險、隨機波動度、波動跳躍等因子，提出新模型以捕捉更多溫度指數之特徵。二、針對不同模型，分別利用最大概似法、期望最大演算法、粒子濾波演算法等進行參數估計。實證結果顯示新模型具有較好之配適能力。三、利用 Esscher 轉換將真實機率測度轉換至風險中立機率測度，並進一步利用 Feynman-Kac 方程式與傅立葉轉換求出溫度模型之機率分配。四、推導冷氣指數／暖氣指數期貨之半封閉評價公式，而冷氣指數／暖氣指數期貨之選擇權不存在封閉評價公式，則利用蒙地卡羅模擬進行評價。五、無論樣本內與樣本外之定價誤差，考慮隨機波動度型態之模型對於溫度衍生性商品皆具有較好之評價績效。六、實證指出溫度市場之市場風險價格為負，顯示投資人承受較高之溫度風險時會要求較高之風險溢酬。本研究可給予受溫度風險影響之產業，針對衍生性商品之評價與模型參數估計上提供較為精準、客觀與較有效率之工具。
This study uses the daily average temperature index (DAT) and market price of the CDD/HDD derivatives for 18 cities from the CME group. There are some contributions in this study: (i) we extend the Alaton, Djehince, and Stillberg (2002)'s framework by introducing the jump risk, the stochastic volatility, and the jump in volatility. (ii) The model parameters are estimated by the MLE, the EM algorithm, and the PF algorithm. And, the complex model exists the better goodness-of-fit for the path of the temperature index. (iii) We employ the Esscher transform to change the probability measure and derive the probability density function of each model by the Feynman-Kac formula and the Fourier transform. (iv) The semi-closed form of the CDD/HDD futures pricing formula is derived, and we use the Monte-Carlo simulation to value the CDD/HDD futures options due to no closed-form solution. (v) Whatever in-sample and out-of-sample pricing performance, the type of the stochastic volatility performs the better fitting for the temperature derivatives. (vi) The market price of risk differs to zero significantly (most are negative), so the investors require the positive weather risk premium for the derivatives. The results in this study can provide the guide of fitting model and pricing derivatives to the weather-linked institutions in the future.
1 Introduction 1
2 Literature Review 7
2.1 Temperature Model 7
2.2 CDD/HDD Derivatives Pricing Model 10
3 The Models 12
3.1 Seasonal Mean-Reversion Model (S-MR) 12
3.2 Seasonal Mean-Reversion Model with Seasonal Volatility (S-MR-S) 13
3.3 Seasonal Mean-Reversion and Jump Diffusion Model with Seasonal Volatility (S-MR-JD-S) 15
3.4 Seasonal Mean-Reversion Model with Seasonal Stochastic Volatility (SMR-S-SV) 16
3.5 Seasonal Mean-Reversion and Jump Diffusion Model with Seasonal Stochastic Volatility (S-MR-JD-S-SV) 18
3.6 Seasonal Mean-Reversion and Jump Diffusion Model with Seasonal Stochastic Volatility and Jump Risk (S-MR-JD-S-SVJ) 19
4 Temperature Derivatives Pricing Formula 21
4.1 Underlying Asset 22
4.2 Temperature Derivatives Markets 23
4.2.1 Chicago Mercantile Exchange 23
4.2.2 Over-the-Counter 25
4.3 Pricing Formula 25
4.3.1 Equivalent Probability Measure 26
4.3.2 Expectation of HDD/CDD Index 29
4.3.3 CDD/HDD Futures Pricing Formula 35
4.3.4 CDD/HDD Futures Options Pricing Formula 35
4.3.5 CDD/HDD Index Options Pricing Formula 37
5 Estimation Method 39
5.1 Maximum Likelihood Estimation (MLE) 40
5.2 Expectation-Maximization (EM) Algorithm 41
5.3 Particle Filter (PF) Algorithm 42
5.3.1 Monte Carlo Filter 43
5.3.2 Resampling 43
5.3.3 Smoothing 44
5.3.4 EM Algorithm 44
6 Empirical Analysis 46
6.1 Data 46
6.1.1 Temperature Index 46
6.1.2 CDD/HDD Futures and Futures Options 48
6.2 Estimated Parameters 49
6.3 Model Performance 50
6.3.1 Market Price of Risk and In-Sample Pricing Performance 51
6.3.2 Out-of-Sample Pricing Performance 53
6.3.3 Comparison of Performances cross Regions 54
7 Conclusions 55
Bibliography 57
Appendix A Change Measure: Deterministic Volatility Model 62
Appendix B Change Measure: Stochastic Volatility Model 64
Appendix C Characteristic Function: Deterministic Volatility Model 67
Appendix D Characteristic Function: Stochastic Volatility Model 69
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