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博碩士論文 etd-0929108-133321 詳細資訊
Title page for etd-0929108-133321
論文名稱
Title
產險公司房價跳躍風險與巨災風險之研究
A essay on the housing price jump risk and the catastrophe risk for the property insurance company
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
77
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2008-09-20
繳交日期
Date of Submission
2008-09-29
關鍵字
Keywords
最大期望演算法、跳躍擴散過程、巨災事件、馬可夫調合普瓦松過程
EM gradient algorithms, jump diffusion processes, catastrophic events, Markov Modulated Poisson process
統計
Statistics
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The thesis/dissertation has been browsed 5755 times, has been downloaded 19 times.
中文摘要
本論文包含兩個研究主題。第一主題探討房價跳躍風險。過去抵押保險契約之定價文獻中,房價過程假設服從幾何布朗運動。然而,若房價過程有明顯跳躍現象,則幾何布朗運動無法捕捉衝擊事件之重要特性。因此,本研究利用EM算法來估計跳躍擴散模型之参數,並採用1986年至2006年之美國月房價資料檢定是否有顯著的跳躍現象。為了獲得較可行之抵押保險契約的定價架構,本文房價過程使用Merton (1976) 跳躍擴散過程。在此模型下,數值分析探討跳躍頻率、跳躍規模之異常波動度以及正常波動度對於抵押保險保費之跳躍風險價格的影響。實證結果顯示跳躍規模的異常波動度對於抵押貸款保費影響最大。
第二主題探討巨災風險。過去文獻假設巨災事件到達率服從普瓦松過程,然而此過程固定頻率之假設並不適用於實際巨災資料,因此本文提出馬可夫調整普瓦松過程以捕捉實際巨災事件到達率過程。在此過程下,狀態服從齊ㄧ的馬可夫鏈,此過程可退化為Cummins and Geman (1993, 1995)、Chang, Chang and Yu (1996)、Geman and Yor (1997) 以及Vaugirard (2003a, 2003b) 之模型。本文應用馬可夫跳躍擴散模型推導出巨災期貨買權、巨災PCS價差買權與巨災債券之封閉解。在實證分析方面,我們利用1950年至2004年PCS 指數與颶風事件發生次數之資料,檢定馬可夫調和普瓦松過程與普瓦松過程之評價巨災商品配適能力。實證結果顯示當評價巨災保險商品時,利用馬可夫調和普瓦松過程描述颶風事件次數的配適能力優於普瓦松過程以及韋柏過程。因此,若不同氣候環境狀態有顯著不同的巨災次數,則利用跳躍擴散模型計算巨災保險商品將產生顯著的定價誤差。
Abstract
This dissertation includes two topics. For the first topic about the housing price jump risk, we use EM gradient algorithms to estimate parameters of the jump diffusion model and test whether the US monthly housing price have jump risk during 1986 to 2006. Then, in order to obtain a viable pricing framework of mortgage insurance contracts, this paper uses the jump diffusion processes of Merton (1976) to model the dynamic process of housing price. Using this model, we investigate the impact of price jump risk on the valuation of mortgage insurance premium from jump intensity, abnormal volatility of jump size and normal volatility. Empirical results indicate that the abnormal volatility of jump size has the most significant impact on the mortgage insurance premium.
For the second topic about the catastrophe risk, we investigate that, for catastrophic events, the assumption that catastrophe claims occur in terms of the Poisson process seems inadequate as it has constant intensity. We propose Markov Modulated Poisson process to model the arrival process for catastrophic events. Under this process, the underlying state is governed by a homogenous Markov chain, and it is the generalization of Cummins and Geman (1993, 1995), Chang, Chang, and Yu (1996), Geman and Yor (1997) and Vaugirard (2003a, 2003b). We apply Markov jump diffusion model to derive pricing formulas for catastrophe insurance products, included catastrophe futures call option, catastrophe PCS call spread and catastrophe bond. We use the data of PCS index and the annual number of hurricane events during 1950 to 2004 to test the quality of the fitting under the Markov Modulated Poisson process and the Poisson process. We reach the conclusion that the Markov Modulated Poisson process is fitter than the Poisson process and Weiner process in modeling the arrival rate of hurricane events when pricing three insurance products. Hence, if different status of climate environment has significant different arrival intensity in real economy, using jump diffusion model to evaluate CAT insurance products could cause significant mispricing.
目次 Table of Contents
Chapter 1: Introduction.....1
1.1. Motivation and contribution in the housing price jump risk......2
1.2. Motivation and contribution in the catastrophe risk ......5
Chapter 2: Literature review to catastrophe-linked products and mortgage insurance contracts...........8
2.1. Mortgage insurance contracts......8
2.2. Catastrophe-linked products.....9
2.3. Literature related to mortgage insurance contracts .....10
2.4. Literature related to catastrophe-linked products .....11
Chapter 3: Estimation of housing price jump risks and impact on the valuation of mortgage insurance contacts.....14
3.1. The contact and model .....14
3.2. Mortgage insurance valuation..... 18
3.3. Estimation via expectation-maximum algorithm...... 21
3.4. Empirical and numerical analysis.....24
Chapter 4: Pricing catastrophe-linked products in Markov jump diffusion models ...... 31
4.1. The model......31
4.2. Valuation of catastrophe-linked products......37 4.3. Empirical and numerical analysis.......46
Chapter 5: Conclusions and further research..... 56
References......59
Appendix ......63
參考文獻 References
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