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研究生:汪昱頡
研究生(外文):Yu-Chieh Wang
論文名稱:跳躍風險下馬可夫轉換模型之實證分析
論文名稱(外文):An Empirical Analysis of Markov Switching Models with Jump Risks
指導教授:林士貴林士貴引用關係
指導教授(外文):Shih-kuei Lin
學位類別:碩士
校院名稱:國立高雄大學
系所名稱:統計學研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:英文
論文頁數:93
中文關鍵詞:馬可夫轉換模型普瓦松跳躍風險之馬可夫轉換模型普瓦松跳躍風險之馬可夫轉換模型EM 演算法概似比檢定法
外文關鍵詞:Markov switching modelMarkov-switching model with Poisson jump risksMarkov-switching model with Markov jump risksExpectation-Maximization algorithmLikelihood ratio test
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Hamilton (1989) 提出馬可夫轉換模型來形容金融變數之時間序列行為,後續實證文獻也證明馬可夫轉換模型可用來解釋經濟上許多現象,例如:經濟循環、股票市場、匯率及短期利率。不幸地,馬可夫轉換模型卻無法形容當偶發事件發生、重大訊息來臨或是重大金融市場衝擊時所造成之跳躍情況,例如:網際網路泡沫化、總體經濟重大消息、亞洲金融風暴等。Merton (1976) 提出跳躍擴散模型以描述資產受到偶發事件影響所發生的不正常跳躍。本文延伸 Hamilton (1989) 和 Merton (1976)模型進而提出兩種模型: (1) 考量普瓦松跳躍風險之馬可夫轉換模型以及 (2) 考量馬可夫跳躍風險之馬可夫轉換模型。此兩種模型可捕捉在不同狀態下,資產價格的平均成長和波動項以及偶發事件發生時之影響。本文將利用Expectation-Maximization (EM) gradient 演算法來估計本文所提的模型參數,並使用概似比檢定法來檢定模型的配適度能力。在實證分析上,本文分析紐約證券交易所(NYSE)的一組樣本,而實證結果發現部分公司之股價平均成長、波動項和不正常跳躍頻率會受所處狀態影響。
Regime-switching models proposed by Hamilton (1989) are well-suited for capturing the time series behavior of many financial variables. Markov-switching models have proved to be quite useful for modeling a range of economic time series, from the business cycle, the stock market, exchange rates, and short-term interest rates. Unfortunately, the Markov switching model can not work well to accommodate jump phenomenon of the occurrence of abnormal events and large shocks to financial market, such as Internet bubble crash, macroeconomic announcement, the Asian and Russian finance crisis. The jump-diffusion model proposed by Merton (1976) can work well to capture the jump risk of asset price when the occurrence of abnormal events. We extend the model of Hamilton (1989) and Merton (1976) to propose two models: Markov-switching model with Poisson jump risks and Markov-switching model with Markov jump risks, which can address the effect that mean and volatility of the stock price depend on the states of business cycle and the jump effect of abnormal events. This paper use the Expectation-Maximization (EM) gradient algorithm to estimate the parameters of the model and use the likelihood ratio statistics to test which model is appropriate. The data consist of 49 NYSE listed stocks. The empirical results show that, in some of the companies, the mean and volatility of the stock price depend on the states of business cycle and the jump effect of abnormal events.
Contents
1. Introduction 1
2. Model of Asset Return 7
2.1 Markov switching model ............................ 7
2.2 Markov switching model with Poisson jump risks ...... 9
2.3 Markov switching model with Markov jump risks ......10
3. Estimation Parameters via EM Algorithm 12
3.1 Estimation parameters of Markov switching model ....... 13
3.2 Etimation parameters of Markov switching model with Poisson
jump risks ....................................... 20
3.3 Estimation parameters of Markov switching model with
Markov jump risks ................................ 22
4. Specification Testing for Models 24
5. Numerical Analysis 27
5.1 Markov switching model ............................27
5.2 Markov switching model with Poisson jump risks ........28
5.3 Markov switching model with Markov jump risks ........29
6. Empirical Analysis 30
7. Conclusions 32
Reference 34
Appendix 39
Table 50
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