<p>Volatility forecast plays a central role in the financial decision making process. An intrinsic purpose of any investor is profit earning. For that purpose investors need to estimate the risk. One of the most efficient</p><p>methods to this end is the volatility estimation. In this theses I compare the CBOE Volatility Index, (VIX) with the actual volatility on an index at the Nordic Market. The actual volatility is defined as the one-day-ahead prediction as calculated by using the GARCH(1,1) model. By using the VIX model I performed consecutive predictions 30 days ahead between February the 2nd, 2007 to March</p><p>the 6th, 2007. These predictions were compared with the GARCH(1,1) one-day-ahead predictions for the same period. To my knowledge, such comparisons have not been performed earlier on the Nordic Market. The conclusion of the study was that the VIX predictions tends to higher values then the GARCH(1,1) predictions except for large prices upward jumps, which indicates that the VIX is not able to predict future shocks.</p><p>Except from these jumps, the VIX more often shows larger value than the GARCH(1,1). This is interpreted as an uncertainly of the prediction. However, the VIX predictions follows the actual volatility reasonable</p><p>well. I conclude that the VIX estimation can be used as a reliable estimator of market volatility.</p>

Volatility forecast plays a central role in the financial decision making process. An intrinsic purpose of any investor is profit earning. For that purpose investors need to estimate the risk. One of the most efficient methods to this end is the volatility estimation. In this theses I compare the CBOE Volatility Index, (VIX) with the actual volatility on an index at the Nordic Market. The actual volatility is defined as the one-day-ahead prediction as calculated by using the GARCH(1,1) model. By using the VIX model I performed consecutive predictions 30 days ahead between February the 2nd, 2007 to March the 6th, 2007. These predictions were compared with the GARCH(1,1) one-day-ahead predictions for the same period. To my knowledge, such comparisons have not been performed earlier on the Nordic Market. The conclusion of the study was that the VIX predictions tends to higher values then the GARCH(1,1) predictions except for large prices upward jumps, which indicates that the VIX is not able to predict future shocks. Except from these jumps, the VIX more often shows larger value than the GARCH(1,1). This is interpreted as an uncertainly of the prediction. However, the VIX predictions follows the actual volatility reasonable well. I conclude that the VIX estimation can be used as a reliable estimator of market volatility.

Τις τελευταίες δεκαετίες η υψηλή μεταβλητότητα που παρατηρείται στις χρηματοοικονομικές μεταβλητές, έχει δημιουργήσει έντονη την ανάγκη για αποτελεσματική διαχείριση του κινδύνου. Τα παράγωγα χρηματοοικονομικά προϊόντα παρέχουν τα μέσα για αντιστάθμιση του κινδύνου. Προς αυτή την κατεύθυνση έχει κατασκευασθεί ένας δείκτης που αντιπροσωπεύει την τεκμαρτή μεταβλητότητα των παραγώγων χρηματοοικονομικών προϊόντων, ο δείκτης VIX. Σκοπός της εργασίας είναι η διερεύνηση της σχέσης του δείκτη VIX με την αγορά του S&P500 και η σχέση συνολοκλήρωσης τεκμαρτής και δεσμευμένης μεταβλητότητας του S&P500. / --

本研究針對台灣地區投資人情緒程度與財經新聞之間的關聯進行研究。本研究以台灣地區發布之恐慌指數(TWVIX)做為投資人情緒程度代理變數。研究樣本期間為2006年12月至2014年12月，新聞資料來源為知識贏家(KMW)。本研究使用文字分析法針對財經新聞內容進行分析，透過計算詞頻和建立語調評分方法來衡量新聞內涵。 本研究之主要發現有：單日媒體發布之新聞數量與恐慌指數呈正相關、單篇新聞平均長度與恐慌指數呈負相關。在文字內容分析的迴歸結果方面，實證結果指出當新聞內的正向字詞使用的越多，投資人情緒程度會降低，相反地，當負向字詞使用的越多，將會提升投資人情緒，產生恐慌狀態。另外，結果也發現當新聞的語調越接近樂觀情緒時，投資人的情緒程度會降低。 本文嘗試了一個新的切入角度來討論金融指標，也就是由新聞媒體效果來探討與恐慌指數之關聯性。本研究結果提供了實證證據證明台灣地區媒體可有效地透過控制財經新聞的內涵，來影響市場上投資人的情緒程度。 / This study examines the relation between investor sentiment and financial news released in Taiwan for the period from Dec. 2006 to Dec. 2014. This study adopts the TAIEX Options Volatility Index (TWVIX) as a proxy for investor sentiment. The study employs the text analysis approach to measure the tone of financial news. The news data is collected from Knowledge Management Winner (KMW) of China Times. The empirical results show that the number of news released on a day has a positive effect on TWVIX; otherwise the length of financial news affects TWVIX negatively. By the text analysis, this study finds that with more positive wording, the degree of investor sentiment is decreased. On the contrary, the quantity of negative words provokes the investor sentiment. Lastly, this research also finds that when the tone of financial news is closer to optimism, it help ease the level of investor sentiment. This research explores a new cut point to discuss the VIX, connecting the issue between a principal financial index and news media in Taiwan. This study believes that the results provide the evidence that Taiwan media actually communicate messages to investors effectively. Thus, news media has the ability to influence investor sentiment no matter by news coverage, words usage and the tone of financial news.

This thesis performs portfolio optimization using three allocation methods, Certainty Equivalence Tangency (CET), Global Minimum Variance (GMV) and Minimum Conditional Value-at-Risk (MinCVaR). We estimate expected returns and covariance matrices based on 7 stock market indices with a DCC-GARCH model including an ARMA (1.1) process and an external regressor of an implied volatility index (VIX). We then simulate returns using a rolling window of 500 daily observations and construct portfolios based on the allocation methods. The results suggest that the model can sufficiently estimate expected returns and covariance matrices and we can outperform benchmarks in form of equally weighted and historical portfolios in terms of higher returns and lower risk. Over the whole out-of-sample period the CET portfolio yields the highest mean returns and GMV and MinCVaR can significantly lower the variance. The inclusion of VIX has marginal effects on the forecasting accuracy and it seems to impair the estimation of risk.

由選擇權價格反推求算出的隱含波動率，可表示市場對未來波動的預期，亦間接反映出該選擇權的價值高低，成為投資者在制定交易策略時重要的依據。經由實證研究發現，CBOE VXO及VIX都可反應投資人的恐慌心理，因此能作為標的走勢的逆向指標，所以又稱為「投資人恐慌指標」。而台指市場並沒有波動率的指標可供投資人參考，所以本研究的目的，是依照臺灣指數選擇權之市場特性，修改多種隱含波動率的估計方法。依照下列比較基準，找出適合台指市場的波動率指數。 1. 報酬反向指標： 分析波動率指數變動與市場報酬之間的關係，觀察「反向非對稱變動行為」，以Vega指數的表現最明顯。 2. 週期行為： 所有波動率指數，在日內行為的偏離幅度都很有限，且週內行為並沒有異常的週期性。分析到期日效果，只有ATM指數在到期日前二日及交易當日顯著下降，顯示台指報酬在到期日前並沒有大幅的異常波動。 3. 預測能力： 比較各波動指數的預測能力優劣。使用避免假性迴歸的模型、每分鐘報價來計算實際波動率，以VIX指數的解釋能力最佳。 綜觀以上分析結果，發現無法找出單一最佳的台指波動率指標。所以若需要最佳的「投資人恐慌指標」，必須使用Vega指數；若想做預測分析，則必須使用VIX指數。

[pt] A presente tese é composta por três pesquisas. A primeira pesquisa buscou averiguar o relacionamento entre o FXvol e os retornos futuros da taxa cambial e do índice de mercado de ações, dado que o índice de volatilidade FXvol é visto como um termômetro da incerteza do investidor um período a frente. Investiga-se então a relação contemporânea entre o FXvol, a Ptax e o Ibovespa, bem como a capacidade do FXvol de captar a possível relação entre o nível de incerteza presente no mercado e as variações relativas futuras da taxa de câmbio e do índice de ações. A segunda pesquisa comparou os modelos GARCH tradicionais e o modelo GARCH com troca de regimes no que tange seu poder de previsão da volatilidade cambial. Buscou-se comparar o desempenho de cada um dos modelos em uma situação real de utilização, no caso, no cálculo do Valor em Risco de uma carteira cambial. A terceira pesquisa buscou identificar a existência do efeito manada no mercado brasileiro e compreender a influência do câmbio nesse efeito, devido à importância do mercado cambial para a realidade brasileira. A metodologia compreendeu dois passos, em um primeiro momento buscou-se analisar a média do efeito através de regressões tradicionais e num segundo momento estudar a variação do efeito ao longo do tempo através do método do Filtro de Kalman. / [en] The present thesis consists of three researches. The first research sought to ascertain the relationship between FXvol and future exchange rate and stock market index returns as the FXvol volatility index is viewed as a thermometer of investor uncertainty for a period ahead. The contemporary relationship between FXvol, Ptax and Ibovespa, as well as the ability of FXvol to capture the possible relationship between the level of uncertainty present in the market and the relative future return of the exchange rate and the stock index. The second research compared the traditional GARCH models and the GARCH model with regime changes regarding its power to predict the exchange rate volatility. We attempted to compare the performance of each of the models in a real situation of use, in this case, in the calculation of the Value at Risk of an exchange portfolio. The third research sought to identify the existence of the herd effect in the Brazilian market and to understand the influence of the exchange rate in this effect, due to the importance of the exchange market for the Brazilian market. The methodology comprised two steps, initially attempting to analyze the mean of the effect through regressions and in a second moment to study the variation of the effect over time through the Kalman Filter method.

台灣特殊的兩黨對立政治環境及幾乎每年都會有的固定選舉，使得政治的不確定性深深的影響著國內的投資環境及投資人心態。本研究便是要探討，2002/1/1~2006/1/16 研究期間台灣的投資人在選舉前後的投資行為，是否真如大家所預期的，會受到台灣選舉事件的影響。 本研究首先利用適當的機率密度函數模型及選擇權市場資訊來導出隱含的風險中立密度值。再利用這些風險中立密度值，求出各個選舉事件相對應的機率分配圖形，並透過其機率分配圖形及波動率指數等統計值於投票日前後的變化來觀察某一選舉事件前後投資者的反應。 研究結果發現：1. 選舉事件的發生確實會影響投資者的心理，且投資者會透過選擇權市場有效率的反應預期的未來股價指數分佈情況。2. 越大型、越具爭議且全國性的選舉結果，其選舉期間機率分配圖形及波動率指數具有較高的波動性。3. 一般而言，選舉過後市場不確定因素降低，將使投資者對於股市的預期較為一致和樂觀。而若這個選舉結果使投資者感到意外，因而增加了市場的不確定性，則選後機率分配圖形及波動率指數的改變反而會更為明顯。4. 在此研究下對數常態混合法比傳統的 Black-Scholes 方法產生較低的誤差值，因此就實證的分析上能提供更好的配適。 / This research examines the behavior of investors during election periods from January 1st 2002 to January 6th 2006 in Taiwan. The research includes a few steps. First, we adopted a proper probability density function composed of stock index options data to construct the implied distribution. Then, when changing the whole shape of the risk-neutral implied distribution, the volatility indexes, and the statistics of the implied distribution, we observed investors' response around a specific election event. According to the empirical results, we found that: 1. An election event would influence investors’ behavior, and investors tend to reflect their expectation of future stock index in the option market in an efficient way. 2. The result of a large-scale and more disputed nationwide election will cause a higher fluctuation in both the implied distribution and the volatility index. 3. In general, the factor resulting from investors’ uncertainty of the market is likely to reduce after the election, which makes investors’ relatively unanimous and optimistic expectation of the stock market. However, if this election result surprises investors, their uncertainty of the market will increase, and thus the changes of the implied distribution and the volatility index become quite obvious. 4. The in-sample performance of the lognormal mixtures method employed in the research is considerably better than that of the traditional Black-Scholes model by having a lower root mean squared error.