本文以次貸風暴期間英國金融服務管理局的限制放空政策為研究對象，探討該政策對股票報酬率、股票波動度之影響。本研究將研究期間分為限制放空期間、允許放空期間，並將英國金融服務管理局公布的限制放空名單劃分為銀行業、財務顧問業、壽險業、產險業，利用GJR模型分析限制放空政策對不同產業影響的差異性。 實證結果證明，除少數銀行類股在限制放空期間的股價報酬率顯著低於允許放空期間，大部分限制放空個股的報酬率在兩期間並無顯著差異，然而限制放空期間幾乎所有研究樣本的股票波動度卻顯著提高。顯見政府限制放空政策不一定能有效抑制股價跌幅，卻會加劇股票波動性，加劇市場震盪。 / UK’s Financial Service Authority banned short selling on financial stocks during subprime crisis. This paper investigates the effects of short-selling restrictions on stocks’ return and volatility in the United Kingdom. After dividing the sample period into banned and no-banned period and classifying the samples into banking, financial consulting, life insurance and nonlife insurance industries, we explore the impact of short-selling restrictions using GJR-GARCH models on individual firms in different industries. We find that stock returns of most samples in the short-selling banned period are not significantly different from the ones in the no-banned period except for a few stocks in the banking industry. However, we also find that stock volatility is significantly higher in short-selling banned period for most samples. Our results show that short-selling restrictions imposed by the U.K. government have only limited effects on stock return, but have significantly alleviated stock volatility.

This dissertation consists of two chapters that examine the construction of financial market volatility indexes and their forecasting efficiency across predictive regression models. Each of the chapter is devoted to diferent volatility measures which are related and evaluated in thframework of forecasting regressions. The first chapter studies the sampling and liquidity issues in constructing volatility indexes, VIX and VXO, in emerging options market like Taiwan. VXO and VIX have been widely used to measure the 22-day forward volatility of the market. However, for an emerging market, VXO and VIX are difficult to measure with accuracy when tradings of the second and next to second nearby options are illiquid. The chapter proposes four methods to sample the option prices across liquidity proxies ¡V five different days of rollover rules ¡V for option trades to construct volatility index series. The paper finds that, based on the sampling method of the average of all midpoints of bid and ask quote option prices, the volatility indexes constructed by minute-tick data have less missing data and more efficient in volatility forecast than the method suggested by CBOE. Additionally, illiquidity in emerging options market does not, based on different rollover rules, lead to substantial biases in the forecasting effectiveness of the volatility indexes.Finally, the forecasting ability of VIX, in terms of naive forecasts and forecasting regressions, is superior to VXO in Taiwan. The second chapter uses high-frequency intraday volatility as a benchmark to measure the efficacy of model-free and model-based econometric models. The realized volatility computed from intraday data has been widely regarded as a more accurate proxy for market volatility than squared daily returns. The chapter adopts several time series models to assess the fore-casting efficiency of future realized volatility in Taiwan stock market. The paper finds that, for 1-day directional accuracy forecast performance, semiparametric fractional autoregressive model (SEMIFAR, Beran and Ocker, 2001) ranks highest with 78.52% hit accuracy, followed by multiplicative error model (MEM, Engle, 2002), and augmented GJR-GARCH model. For 1-day forecasting errors evaluated by root mean squared errors (RMSE), GJR-GARCH model augmented with high-low range volatility ranks highest, followed by SEMIFAR and MEM model, both of which, however, outperform augmented GJR-GARCH by the measure of mean absolute value (MAE) and p-statistics (Blair et al., 2001).

In this thesis we use the GARCH(1,1) and GJR-GARCH(1,1) models to estimate the conditional variance for five equities from the OMX Nasdaq Stockholm (OMXS) stock exchange. We predict 95% and 99% Value-at-Risk (VaR) using one-day ahead forecasts, under three different error distribution assumptions, the Normal, Student’s t and the General Error Distribution. A 500 observations rolling forecast-window is used on the dataset of daily returns from 2007 to 2014. The empirical size VaR is evaluated using the Kupiec’s test of unconditional coverage and Christoffersen’s test of independence in order to provide the most statistically fit model. The results are ultimately filtered to correspond with the Basel (II) Accord Penalty Zones to present the preferred models. The study finds that the GARCH(1,1) is the preferred model when predicting the 99% VaR under varying distribution assumptions.

This essay investigates three different GARCH-models (GARCH, EGARCH and GJR-GARCH) along with two distributions (Normal and Student’s t), which are used to forecast the Value at Risk (VaR) for different return series. Seven major international equity indices are examined. The purpose of the essay is to answer which of the three models that is better at forecasting the VaR and which distribution is more appropriate.  The results show that the EGARCH(1,1)  is preferred for all indices included in the study.

No / This study investigates the impact of LIFFE's introduction of individual equity futures contracts on the risk characteristics of the underlying stocks trading on the LSE. We employ the Fama and French three-factor model (TFM) to measure the change in the systematic risk of the underlying stocks which arises subsequent to the introduction of futures contracts. A GJR-GARCH(1,1) specification is used to test whether the futures contract listing affects the permanent and/or the transitory component of the residual variance of returns, and a control sample methodology isolates changes in the risk components that may be caused by factors other than futures contract innovation. The observed increase (decrease) in the impact of current (old) news on the residual variance implies that futures contract listing enhances stock market efficiency. There is no evidence that futures innovation impacts on either the systematic risk or the permanent component of the residual variance of returns.

No / This study assesses whether the widely documented momentum profits can be ascribed to time-varying risk as described by a GJR-GARCH(1,1)-M model. Consistent with rational pricing in efficient markets, we reveal that momentum profits are a compensation for time-varying unsystematic risks, common to the winner and loser stocks. We also find that, because losers have a higher propensity than winners of disclose bad news, negative return shocks increase their volatility more than it increases that of the winners. The volatility of the losers is also found to respond to news more slowly, but eventually to a greater extent, than that of the winners. Following Hong et al. (2000), we interpret this as a sign that managers of loser firms are reluctant to disclosing bad news, while managers of winner firms are eager to releasing good news

Volatility is an important variable in financial markets, risk management and making investment decisions. Different volatility models are beneficial tools to use when predicting future volatility. The purpose of this study is to compare the accuracy of various volatility models, including ARCH, GARCH and extensions of the GARCH framework. The study applies these volatility models to the Swedish and American Fixed Income Market for government bonds. The performance of these models is based on out-of-sample forecasting using different loss functions such as RMSE, MAE and MSE, specifically investigating their ability to forecast future volatility. Daily volatility forecasts from daily bid prices from Swedish and American 2, 5- and 10-year governments bonds will be compared against realized volatility which will act as the proxy for volatility. The result show US government bonds, excluding the US 2 YTM, did not show any significant negative volatility, volatility asymmetry or leverage effects. In overall, the ARCH and GARCH models outperformed E-GARCH and GJR-GARCH except the US 2-year YTM showing negative volatility, asymmetry, and leverage effects and the GJR-GARCH model outperforming the ARCH and GARCH models. / Volatilitet är en viktig variabel på finansmarknaden när det kommer till både riskhantering samt investeringsbeslut. Olika volatilitets modeller är fördelaktiga verktyg när det kommer till att göra prognoser av framtida volatilitet. Syftet med denna studie är att jämföra det olika volatilitetsmodellerna ARCH, GARCH och förlängningar av GARCH-ramverket för att ta reda på vilken av modellerna är den bästa att prognosera framtida volatilitet. Studien kommer tillämpa dessa modeller på den svenska och amerikanska marknaden för statsskuldväxlar. Prestandan för modellerna kommer baseras på out-of-sample prognoser med hjälp av det olika förlustfunktionerna RMSE, MAE och MSE. Förlustfunktionernas används endast till att undersöka deras förmåga till att prognostisera framtida volatilitet. Dagliga volatilitetsprognoser baseras på dagliga budpriser för amerikanska och svenska statsobligationer med 2, 5 och 10 års löptid. Dessa kommer jämföras med verklig volatilitet som agerar som Proxy för volatiliteten. Resultatet tyder på att amerikanska statsobligationer förutom den tvååriga, inte visar signifikant negativ volatilitet, asymmetri i volatilitet samt hävstångseffekt. De tvååriga amerikanska statsobligationerna visar bevis för negativ volatilitet, hävstångseffekt samt asymmetri i volatiliteten. ARCH och GARCH modellerna presterade övergripande sett bäst för både svenska och amerikanska statsobligationer förutom den tvååriga där GJR-GARCH modellen presterade bäst.

Volatility managing strategies have gained attention over the last few years due to theiralleged ability to increase portfolio return and mitigate risk. This thesis examines the performance and risk of a portfolio using such a strategy on the Swedish equity market. The strategy is dependent on the forecasting of volatility. Different volatility forecasting models are evaluated using different refitting intervals. The GARCH(1,1) model using a monthly refitting interval is found to be the most precise. When comparing it to the buy-and-hold portfolio, the results of the risk and return of the portfolio are ambiguous and the volatility managing strategy is only found to be beneficial when using a fixed volatility target when transaction costs are accounted for. Regarding distributional characteristics, the volatility managing strategy displays features of a lighter-tailed distribution in comparison to the buy-and-hold portfolio when using a dynamic volatility target. However, for the fixed target, the distributional characteristics are incoherent. Lastly, the volatility managing strategy is not found beneficial to the investor during a shorter period of high volatility. This thesis provides support for using a volatility managing strategy with a fixed volatility target for generating a higher return compared to the benchmark. However, it does not support conclusive evidence for obtaining a higher return without increasing the risk level of the investment. / Användningen av volatilitetshanterande strategier har fått ökad uppmärksamhet under de senaste åren. Därför undersöker detta arbete avkastningen och risken hos en portfölj som använder en sådan strategi på den svenska aktiemarknaden. Investeringsstrategin är baserad på prognosen av volatilitet. Olika modeller för volatilitetsprediktion utvärderas för olika tidsintervall för att hitta modellen med högst precision. Denna studie finner att en GARCH(1,1) modell som omanpassar sig månadsvis resulterar i den mest exakta prediktionen. Med hänsyn till risk och avkastning så är resultaten för volatilitetsstrategin tvetydiga i jämförelse med en köp-och-behåll strategi. Volatilitetsstrategin är endast fördelaktig när ett fast volatilitetsmål används då transaktionskostnader inkorporeras. Med avseende på fördelningsegenskaper, så visar en volatilitetsstrategi med ett rörligt volatilitetsmål på egenskaper hos en fördelning med lättare svansar, i jämförelse med köp-och-behåll portföljen. För det fasta volatilitetsmålet så är fördelningsegenskaperna inkoherenta. Volatilitetsstrategin är inte fördelaktig för investeraren under en kortare period med hög volatilitet. Detta examensarbete ger underlag för användandet av en volatilitetshanterande strategi med ett fast volatilitetsmål för att uppnå en högre avkastning i relation till referensportföljen. Det bevisar dock inte att en högre avkastning går att uppnå utan att öka risken hos portföljen.

Time series forecasting and volatility forecasting is a particularly active research field within financial mathematics. More recent studies extend well-established forecasting methods with machine learning. This thesis will evaluate and compare the standard Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model and some of its extensions to a proposed Long Short-Term Memory (LSTM) model on historic data from five Swedish stocks. It will also explore hybrid models that combine the two techniques to increase prediction accuracy over longer horizons. The results show that the predictability increases when switching from univariate GARCH and LSTM models to hybrid models combining them both. Combining GARCH, Glosten, Jagannathan, and Runkle GARCH (GJR-GARCH), and Fractionally Integrated GARCH (FIGARCH) yields the most accurate result with regards to mean absolute error and mean square error. The forecasting errors decreased with 10 to 50 percent using the hybrid models. Comparing standard GARCH to the hybrid models, the biggest gains were seen at the longest horizon, while comparing the LSTM to the hybrid models, the biggest gains were seen for the shorter horizons. In conclusion, the prediction ability increases using the hybrid models compared to the regular models. / Tidsserieprognostisering, och volatilitetsprognostiering i synnerhet, är ett växande fält inom finansiell matamatik som kontinereligt står inför implementation av nya tekniker. Det som en gång startade med klassiksa tidsseriemodeller som ARCH har nu utvecklats till att dra fördel av maskininlärning och neurala nätverk. Detta examensarbetet uvärderar och jämför Generalized Autoregressive Conditional Heteroskedasticity (GARCH) modeller och några av dess vidare tillämpningar med Long Short-Term Memory (LSTM) modeller på fem svenska aktier. ARbetet kommer även gå närmare inpå hybridmodeller som kombinerar dessa två tekniker för att öka tillförlitlig prognostisering under längre tidshorisonter. Resultaten visar att förutsägbarheten ökar genom att byta envariata GARCH och LSTM modeller till hybridmodeller som kombinerar båda delarna. De mest korrekta resultaten kom från att kombinera GARCH, Glosten, Jagannathan, och Runkle GARCH (GJR-GARCH) och Fractionally Integrated GARCH (FIGARCH) modeller med ett LSTM nätverk. Prognostiseringsfelen minskade med 10 till 50 procent med hybridmodellerna. Specifikt, vid jämförelse av GARCH modellerna till hybridmodellerna sågs de största förbättringarna för de längre tidshorisonterna, medans jämförelse mellan LSTM och hybridmodellerna sågs den mesta förbättringen hos de kortare tidshorisonterna. Sammanfattningsvis öker prognostiseringsförmågan genom användning av hybridmodeller i jämförelse med standardmodellerna.

過去文獻在探究利率波動行為時多採用現貨市場利率做為研究對象，思及期貨市場交易成本較低且流動性也較高使其對新資訊的反應更為迅速下，本文改以短期利率期貨，三個月期歐洲美元定存利率期貨、三個月歐元存款利率期貨以及三十天期商業本票利率期貨的隱含利率作為樣本資料，進而探討美國、歐洲及台灣的利率波動行為。研究方法以Gray(1996)提出的一般化狀態轉換模型為基礎並加入可以反應不對稱性的Dispersion設定，此設定有二個優點，其一為當面臨極大衝擊時，可減少衝擊所造成的變異數持續性而產生波動度均數復歸的現象，此設計乃考量到樣本期間一半時期均處於高峰度狀態的情形不常見，當波動度處於高峰時，預期市場波動度會反轉成近似常態水準；其二為易於Student’s t分配之狀態轉換模型下自由度的參數化設定，使峰態可隨狀態轉換。另外亦加入槓桿效果設定來反應市場上正負消息對資產報酬波動度所造成的不對稱影響。 由AIC模型配適度選擇準則下，適合描述美國、歐洲以及台灣的利率模型分別為RS-GARCH-L-DF, RS-GJR-GARCH-L-DF與RS-GJR-GARCH模型，這三個模型在DM預測力檢定下亦顯示具較佳模型預測力，本文進一步透過此些模型來探測歷年來重大經濟事件與央行利率政策對利率波動度的影響與關聯性。 研究結果顯示美國、歐洲及台灣的利率波動行為均具有顯著的高低兩波動狀態，台灣與歐洲的利率處於高低波動期間的機率較平均，但台灣處於高波動度狀態的機率遠高於歐洲，相形之下，美國普遍處於低波動度狀態；三者的利率長期皆會回歸於某一均衡水準，且顯著存在波動度叢聚的現象，其中，台灣利率的波動最為劇烈，而美國與歐洲的利率行為則具有波動度長期會回歸某一均衡水準的現象。當利率水準較高時，可清楚窺知歐洲的利率波動度也會較大，此現象亦存在於美國的高波動時期，但不適用於台灣利率動態行為上的描述。