Threshold and Leverage Effects of Major Asian Stock Markets Based on Stochastic Volatility Models

[[abstract]]市場波動是一種重要的金融風險衡量指標，並且其對於很多金融決策過程扮演著決定性的角色，例如：選擇權定價，避險策略，投資組合配置和風險值 (Vale-at-risk) 計算。隨著國際金融市場連動的擴大與跨國境資金的自由化流動的加深，在美國和東亞之間的國際資金流動已經變得越來越普遍。在這越來越全球化的金融環境下，一個金融市場的擾動會立即地會影響全球金融系統。本研究旨在探討此一現象，方法上我們延伸隨機波動(Stochastic Volatility) 模型以考慮一國股票市場對於本國及國際股市衝擊下複雜的市場反應。本研究拓展隨機波動模型致一個更複雜更一般化的設定。本研究發展兩種新類型的隨機波動模型：（一）含有門檻影響 (Threshold effect) 的隨機波動模型 (TSV 模型)，（二）包含有門檻和槓桿效果 (Leverage effect) 的隨機波動模型 (TLSV 模型)。本研究使用馬可夫鏈蒙第卡羅法(Markov Chain Monte Carlo： MCMC)來估計模型，以達到較精確的參數與波動的估計。本研究的實證結果將可以顯示亞洲金融市場間一些有趣的金融現象，作為國際投資人避險與資產配置的參考。我們也將利用一些統計準則來比較此兩類模型對於資料的配適度。[[abstract]]Market volatility is a measure of financial risks, and plays a crucial role in financial decision-making, option pricing, hedging strategies, portfolio allocation and Value-at-Risk calculations. This study extends stochastic volatility (SV) models to consider these complex market responses to local and international return shocks. The SV models are extended to a more complex setting. Two types of SV models, the SV model with threshold effects (TSV model) and the SV model with both threshold and leverage effects (TLSV model), are used in this study. These models are estimated using a Markov Chain Monte Carlo (MCMC) method. The empirical results of this study may reveal some interesting phenomenon among major Asian financial markets. We will also compare the model fitting of these two types of models in terms of some criterions

Integrating Spectral Clustering with Wavelet-Based Kernel Partial Least Square Regressions for a Dynamic Financial Forecasting and Trading System

[[abstract]]財務預測和交易決策是現代時間數列資料採礦中極富挑戰性的應用領域，為金融機關與企業成功獲利的根本條件。然而，因著國際金融市場的擴展與連動性的增強；另一方面，跨國界現金流動持續地增加與自由化，國際金融市場之互動關聯越來越緊密，此一連動現象有助於投資者預測未來全球指數的走勢並建構優秀的投資決策系統。本研究的目地即在建立一個以小波分析為基礎能夠萃取國際金融市場連動特徵，融合新進的核空間迴歸法，所建構之可靠精確的投資決策專家系統。本研究計畫建構之新穎性專家系統規劃如下：在資料輸入的第一級，多國籍股價指數首先經由小波分析（Wavelet Analysis）分解，變換原始資料空間至一個多重時間表尺度的特徵空間，此一空間較適合作為財務預測之使用；接著再以這些萃取的多維多時間尺度特徵進行頻譜式集群（Spectral Clustering）分析，將特徵空間依其時間數列動力特徵拆解成幾個互不相交的獨立區域，以匯集不同的股價型態區域。在第二階段，多個核空間偏最小二乘式迴歸（multiple kernel partial least square regressors）分別配適步驟一的不同區域，形成多重專家網路做出最後的預測與投資決策。與傳統類神經網絡、純粹的SVM（Support Vector Machine）或者是GARCH（Generalized autoregressive conditional heteroscedasticity）模型比較，我們預期本研究所提出的模型將達到最好的績效，獲得最高的報酬。[[abstract]]Financial predictions and tradings are challenging applications of modern time series data mining, which are essential for the success of many businesses and financial institutions. However, with the expansion of international financial links and the continued liberalization of cross-border cash flows, the increasingly tight correlations among financial markets help investors for making good forecasts and trading decisions on the co-movements of stock price indices. The objective of this study is to implement a new expert system that could extract key features among international financial markets to make good predictions and trading decisions. The novel expert system will be implemented in this study is as follows: in the first stage, wavelet analysis transforms the input space of raw data to a time-scale feature space suitable for financial forecasting, and then a spectral clustering algorithm is used for partitioning the feature space into several disjointed regions according to their time series dynamics. In the second stage, multiple kernel partial least square regressors (KPLSRs) that best fit partitioned regions are constructed for final forecasting. Compared with neural networks, pure SVMs (Support Vector Machines) or traditional GARCH (Generalized autoregressive conditional heteroscedasticity) models, we expect the proposed model will perform best and achieve the highest profit

Online Forecasting of Option Prices by Using Particle Filters and Support Vector Machines

[[abstract]]這篇研究提出了多期望準位(multi-aspiration levels)的新概念，取代了傳統目標規劃法(goal programming)只能有一個期望準位，如此更易於解決多目標的問題。根據此新想法，它能夠應用多期望準位的技術於目標規劃法上。使用多期望準位在目標規劃法上的主要貢獻為，它可以幫助決策制定者，對於其決策或管理上的問題制定出最佳或最適合的政策。除此之外，在目標規劃上的期望準位不在只可以設定為純量，也可以設定為向量和函數了。上述的方法能改善目標規劃在解決真實問題上的實際使用性。最後，我們會使用一些實務上的範例來驗證所提出模型的應用性

Returns and Volatility Contagions over Different Time Scales between S&P 500 and Major Asian markets Indices

[[abstract]]本研究將探討S&P 500 與亞洲主要指數之報酬率與波動的互動情形。。我們將採用以小波分析 (wavelet analysis) 為基礎的多維度隨機波動 (multivariate stochastic volatility) 模型來探討各指數間的相關性與傳播效果，亦即本研究將採用多維度隨機波動模型分別分析原始資料與小波分解資料，並比較兩種分析結果。以往缺乏計量分析的工具，在經濟分析上一般僅能做到長短期的均衡分析。但是在財務經濟上，尤其是股票市場的分析，這樣的分析顯然不足，因為在國際股票市場上參與的投資客各形各色，從短線套利的對沖基金 (Hedge fund) 到長線投資的退休基金都有。可以預期各型投資人有他們各自決策的時間尺度，因而整合起來整個市場會有各種不同時間尺度的波動。要分析這樣的現象，多維度隨機波動模型顯然優於傳統multivariate GARCH 模型，但可以預見地單單只採用多維度隨機波動模型仍無法令人滿意，小波分析正足於彌補這樣的不足。小波分析提供時間尺度的放大鏡，讓我們分解從帽客、極短線、短線、中線、長線各型投資人行為所引起的波動，再輔以多維度隨機波動模型來探討這些指數間的互動關連。可以預期小波分解資料中將含有更多各時間尺度投資人的行為反應，而multivariate stochastic volatility 可以幫助我們瞭解各群投資人的行為模式

An Intelligent Credit Forecasting and Decision Support System--- Integrating Supervised Maximum Variance Unfolding and Kernel Classifiers

[[abstract]]巴賽爾銀行監理委員會 (Basel Committee on Banking Supervision) 於 2001年提出『新巴賽爾資本協定』，要求全球金融機構建立內部信用評等評估系統，以精確評量其持有資產部位隱含之信用風險，於是信用風險管理議題為當前學界與業界所重視。再則2007年下半年以來，次級房貸風暴興起，嚴重打擊美國銀行業，更加深金融機構對智慧型信用評等系統之殷切需求，藉以提供其內部進行風險管理與授信決策之依據。目前擁有最準確信貸風險評估決策系統的銀行，將是最賺錢的銀行。進行信用評等分類時，由於輸入變數是高維度的財務資訊，經常需面對降低資料維度的問題。最大變異展開 (Maximum Variance Unfolding，MVU) 是集群分析方面最有效的非線性降維法之一。本研究計劃結合一新的監督式版本的最大相異展開法 (Supervised-MVU，S-MVU) 與多種核空間分類器（Kernel Classifier） (著名的核空間分類器如支援向量機，Support Vector Machine，SVM) 發展一個全新的智慧型信貸等級評估系統︰首先，S-MVU 降低非線性輸入資料的維度，然後核空間分類器進行最後的分類。S-MVU利用類別資訊導引代表性低維流形或子空間之建立，可有效對付資料中之雜訊。我們預期實證的結果將顯示本研究之智慧型預測系統將勝過純核空間分類器與傳統的分類器(例如：貝氏網路，羅吉式回歸和最小近鄰法)。與其他降維法相比，S-MVU對於分類器的性能提升是顯著而穩健的。[[abstract]]The New Basel Accord for bank capital regulation is designed to better align regulatory capital to the underlying risks by encouraging better and more systematic risk management practices, especially in the area of credit risk. Credit rating forecasting had been a critical issue in the banking industry. All banking institutes and their regulators attempt to search for a precise internal credit system to capture the credit quality of their evaluation borrowers. Furthermore, subprimemortgage crisis in the later half of 2007 have heavily threatened the U.S. banking sector. Credit risk profoundly impacts the banking sector. The bank with the most accurate estimation of its credit risk will be the most profitable. When performing credit rating classification, one often confronts the problem of dimensionality reduction due to the high dimensional financial input data. Maximum variance unfolding (MVU) is one of the most promising nonlinear dimensionality reduction techniques in clustering. By integrating a supervised variant of maximum variance unfolding (S-MVU) with kernel classifiers (such as support vector machines, SVMs), this study develops a new model for credit rating forecasting: first, S-MVU reduces the high dimensionality of nonlinear distributed input data, and then kernel classifiers perform the final classification. Using the class information of given data to guide the manifold learning, S-MVU helps to deal with the noise in the data and thus makes kernel classifiers more robust in classification. Empirical results will indicate that kernel classifiers with S-MVU outperform pure kernel classifiers and traditional classifiers such as Bayesian networks, logistic regressions, and the nearest neighbors method. Compared with other dimensionality reduction methods the performance improvement owing to S-MVU is significant and robust

Pricing Credit Derivatives under Different Information Sets

本論文包含兩大主題，主要探討投資人在不同訊息集合下，如何訂價信用型衍生性商品與公司債信用價差。本論文有效地結合信用風險兩大主流評價模型– 精簡模型（reduced form model）與結構模型（structural form model），亦即採用精簡模型為基礎，再適度結合結構模型中之直觀經濟意義，來評價相關的商品。論文前後兩部分分別考慮投資人面臨的兩種情境，論文第一部份考慮投資人面對窗飾之財務報表，在不完全資訊下，如何從市場交易資訊中，估測公司真實財務體質，以評價該公司之信用型衍生性商品。由實際數值模擬所展現的結果顯示，這些由不完全資訊所產生的額外信用價差，在長到期日的衍生性商品下，是相當顯著的。 本論文第二部分本文主要探討投資人若具有擴大的訊息集合，亦即其訊息集合中具有某種預期性或內線型訊息，則評價一公司債的信用價差會具有何種期間結構。本部分論文中，我們展示如何將內線訊息加入傳統的隨機架構之中，並探討投資人在不真實財務報表下，信念更新與對內線消息的預期效果。在本文模型下， 確實改進傳統結構模型的重大缺點，即短到期日下，信用價差明顯過小的問題。The thesis includes two articles. These two articles focus on the same issue--how to pricing credit derivatives and credit spreads under different information sets. These two articles all employ reduced models as a base framework, and combine intuitions from structural models to consider the pricing problems. But they consider different situations an investor may face, the first article focus on the situation when investors only possess a firm's noisy financial report (incomplete information). We develop methods to infer the company's real financial constitution from market trading data. The second article considers the situation when an investor's information set is enlarged to include anticipative information. Conditioning on the extended information set, we show how to incorporate the insider information into the original model, and thus give us a better estimation of the firm's survival probability.Contents 1. Introduction ………………………………………………………..… 1 2. Pricing Credit Derivatives under Incomplete Information ……….. 3 2.1 Introduction …………………………………………………….. 3 2.2 Preliminaries …………………………………………………… 9 2.3 State Variables of Default Risk ………………………………… 13 2.4 Credit Derivatives ……………………………………………… 18 2.5 Learning Process ……………………………………………….. 21 2.6 Numerical Results ……………………………………………… 25 2.7 Conclusion ……………………………………………………… 43 3. Term Structure of Credit Spreads with Anticipation Effects …….. 45 3.1 Introduction …………………………………………………….. 45 3.2 The General Framework ……………………………………….. 48 3.3 Anticipations from Derivative Markets ……………………….. 50 3.4 Learning Effects on Market Information ……………………… 59 3.5 Numerical Results ……………………………………………... 61 3.6 Conclusion …………………………………………………….. 69 4. Conclusion …………………………………………………………. 71 Appendix ………………………………………………………………... 72 References ………………………………………………………………. 74 Figures Figure 1: Default Probability I ……………………………..……..… 27 Figure 2: Default Probability I …………………………….…..…….. 28 Figure 3: Zero Recovery Defaultable Bond Price I………..…....…….. 31 Figure 4: Zero Recovery Defaultable Bond Price II………..…….…….. 32 Figure 5: Default Digital Put Option Price I ………………..………….. 34 Figure 6: Default Digital Put Option Price II ………………..…..…….. 35 Figure 7: Survival Probability under Incomplete Information ..……….. 39 Figure 8: Zero Recovery Defaultable Bond Price under Incomplete Information ..………………………………………………. 40 Figure 9: Default Digital Put Option Price under Incomplete Information ..………………………………………….….. 41 Figure 10: Credit spreads under information of terminal asset value V_T ..………………………………..………………….….. 63 Figure 11: Conditional survival probabilities under information of terminal asset value V_T ..…………..………………….….. 64 Figure 12: Credit spreads under extended information of terminal asset value points distribution I ….…..………………….….. 65 Figure 13: Conditional survival probabilities under extended information of terminal asset value points distribution I .…………….….. 66 Figure 14: Credit spreads under extended information of terminal asset value points distribution II ….…..………………….….. 67 Figure 15: Conditional survival probabilities under extended information of terminal asset value points distribution II .…………….….. 68 Tables Table 1: Parameters Used in Numerical Analysis ……………..………… 26 Table 2: Parameter Impact Analysis ………………………….…..…….... 30 Table 3: Default Put Option Prices ………………..………..…....…….... 36 Table 4: Credit Default Swap Spreads ……………………..…….…….... 37 Table 5: Parameter Impact Analysis on V^DP and CDS Spreads ………. 37 Table 6: Default Put Option Prices under Incomplete Information ….….. 42 Table 7: CDS Spreads under Incomplete Information ..………………….. 4

交易量在估計期貨市場動態極端風險值的角色

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