跳到主要內容

簡易檢索 / 詳目顯示

回結果列表
研究生： 李權峰
Chuan-Fong Lee
論文名稱： 在混和常態模型下使用貝氏方法估計參數在股票和選擇權資料
Bayesian parameter estimation using stock and option data under Mixture Normal Models
指導教授： 傅承德
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 統計研究所
Graduate Institute of Statistics
論文出版年： 2017
畢業學年度： 105
語文別： 英文
論文頁數： 36
中文關鍵詞： 混合常態模型 、隱含波動率 、貝氏估計 、信賴區間 、選擇權市場 、股票市場
相關次數： 點閱：22  下載：0 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 本文中，我們引用了一個混合常態模型來分析股票市場跟選擇權市場的關係。觀察在加入隱含波動率的訊息之後，混合常態模型的波動率是否有影響，而我們檢驗的方式是建立信賴區間去看他的變化，在模擬跟實證都是使用的是貝氏估計來探討，最後發現加入隱含波動率這個動作，確實減少了混合常態模型整體
    波動率的信賴區間長度，估計值也變精準，也說明了選擇權跟股票市場在混合常態模型估計下會互相影響。

    In this paper, we use a mixture normal model to analyze the relationship between the stock market and the option market. Observe after adding the implied volatility, whether the volatility of the mixture normal model has an effect and the way we test is to establish a confidence interval to see its changes. In the simulation and empirical study are using the Bayesian estimate to explore. Finally found to join the implied volatility, does reduce the confidence interval length of total volatility and estimates are more accurate, also shows that the option and the stock market under the mixture normal model will affect each other.

    摘要 i Abstract ii 誌謝 iii 1 Introduction 1 2 MNModelandImpliedVolatility 3 2.1 MixtureNormalModel.............................3 2.2 ImpliedVolatility................................6 3 Theparametersestimation 7 3.1 Bayesianwithstock..............................7 3.2 Bayesianwithstockandoption........................10 4 Simulations 13 4.1 Step.......................................13 4.2 Simulationresults................................17 5 Empiricalstudy 20 5.1 Datadescription................................20 5.2 Empiricalresult.................................21 6 Conclusion 25 References 26

    [1] Alexander,C.,Narayanan,S.,(2001)OptionPricingwithNormalMixtureReturns
    ModellingExcessKurtosisandUncertaintyinVolatility. ICMA CentreDiscussion
    PapersinFinance.
    [2] Ehlers,R.S.,(2003)BayesianInferenceandMCMCmethods:nopain,noWindows.
    [3] Efron,B.(2013)EmpiricalBayesmodeling,computation,andaccuracy.
    [4] Gen¸cay,R.,Salih,A.,(2003)DegreeofMispricingwiththeBlack-ScholesModel
    and NonparametricCures. ANNALS OFECONOMICSANDFINANCE, 4,73-101.
    [5] Huang,Y.L.(2015)BayesianReliabilityAnalysisofConstant-StressAccelerated
    Degradation BasedonGammaProcesswithRandomEffectandTime-ScaleTrans-
    formation.
    [6] Ismail,M.T.,Phoong,S.Y.,(2015)AComparisonBetweenBayesianandMaximum
    LikelihoodEstimationsinEstimatingFiniteMixtureModelforFinancialData. Sains
    Malaysiana, 44(7), 1033–1039.
    [7] Joseph,R.R.,(1981)MIXTURESOFNORMALDISTRIBUTIONSANDTHE
    IMPLICATIONSFOROPTIONPRICING.
    [8] Kon,S.J.,(1984)ModelsofStockReturns:Finance,39,147-165.
    [9] Kon,S.,(1984)ModelsofStockReturns-AComparison. The JournalofFinance,
    39, 147-165.
    [10] Macbeth,J.D.,Merville,L.J.,(1979)AnempiricialexaminationofBlack-Scholes
    call optionpricingmodel. The JournalofFinance, 34,1173-1186.
    [11] Näsholm,A.,Bunjaku,B.,(2010)ForecastingVolatility-AComparisonStudyof
    ModelBasedForecastsandImpliedVolatility.
    [12] Neumann,N.,(1997)OptionPricingundertheMixtureofDistributionsHypothesis.
    DiskussionspapierNr.208.
    [13] Ornthanalai,C.,(2014)Lévyjumprisk:Evidencefromoptionsandreturns. Journal
    of FinancialEconomics, 112, 69-90.
    [14] Polson,N.,Johannes,M.,(2006)MCMCMethodsforContinuous-TimeFinancial
    Econometrics.
    [15] Poon,S.H.,(2005)APracticalGuidetoForecastingFinancialMarketVolatility.
    [16] Popovi´c,B.V.,Cordeiro,G.,Ortega,E.M.,Pascoa,M.A.R.,(2017)Anewex-
    tended mixturenormaldistribution. MATHEMATICALCOMMUNICATIONS, 22,
    53–73.
    [17] Redner,R.A.,Walker,H.F.,(2009)MixtureDensities,MaximumLikelihoodand
    the EmAlgorithm.In SIAM Review, Vol.26,195-239.
    [18] Tomczak,J.M.(2012)FisherinformationmatrixforGaussianandcategoricaldis-
    tributions.
    [19] Xu,D.,Wirjanto,T.S.,(2009)TheApplicationsofMixturesofNormalDistributions
    in EmpiricalFinance:ASelectedSurvey.
    [20] Zucchini,W.,MacDonald,I.(2009)HiddenMarkovModelsforTimeSeries.

    QR CODE
    :::