Modelling the VaR Combined with Extreme Value Theory and Markov Regim-Swithing Process

碩士論文[[abstract]]風險值的興起已行之有年，利用常態分配假設之下的風險值模型亦相當多；但模型常因政經趨勢的改變而不同，導致風險值評估上的不準確，造成許多金融事件發生。在傳統的計量模型上，對於報酬具有後尾的現象無法有效的顯現，因其建構基礎皆架構在常態分配假設之下；而後發展出非固定分配假說的極值理論；雖然極值理論有非特定分配的優點，可以捕捉到瞬間的風險狀況，但對長期的影響依然無法獲得充分的詮釋。而隨狀態改變分配的馬可夫轉換過程，正是可以改善的作法。有鑒於此，本文結合在特定條件下可轉換狀態的馬可夫過程與可解釋厚尾現象的極值理論，以作為風險值評估時的分配模型。本研究利用S&P500指數進行研究，研究發現，在模型的概似函數值上有很明顯的差異，並且與傳統上的GARCH模型做比較時，配適的程度高出許多，顯見對於風險值的估計相當有幫助。[[abstract]]The Value-at-Risk starts the line for many years, there are many risk value model for using normal distribution supposition, but these models always changed by following political and the economical tendency, which are leading inaccuracy of Value-at-Risk estimate, afterward making financial incidents. In traditional measurement model, remuneration distribution that has thick tail phenomenon cannot effective to appear, because of it based on normal distribution supposition, then developing the extreme value theory which is non-regular distribution. Although, extreme value theory has an advantage can get risk degree in moment, but it cannot fully explain long term influence. However, Markov switching model has specified characteristic, which changes distribution by state, is exactly the practice method which can be improved. In view of this, this article unifies under the specific condition may transform the condition for Markov process with to be possible to explain the thick tail phenomenon extreme value theory. This article utilizes S&P500 index to carry out the result, has found there are some significant difference in the likelihood function value and compared with traditional GARCH model, MRS-GEVD will get the better suitable degree, can help the risk value estimate