Even though major advances in economic theory and modelling have in some cases furthered our understanding of how the economy works, the system as a whole has become more complex. If policymakers had perfect knowledge about the actual state of the economy, the various transmission mechanisms as well as the true underlying model, monetary intervention would be greatly simplified. In reality, however, the monetary authorities have to contend with considerable uncertainty in relation to the above-mentioned factors. This said, uncertainty has mostly been neglected in both the theoretical and empirical literature focusing on monetary policy analysis. Nonetheless, findings from a review of theoretical literature that does exist on this topic suggest that optimal central banks act more conservatively when faced with uncertainty. Similarly, empirical findings from the literature also favour conservatism. However, there is some evidence to suggest that this is not always the case. These results suggest that central banks do not always act optimally when faced with uncertainty. The limited number of industrial country cases examined prevents any generalised view from emerging. If anything, the literature findings suggest that central bank behaviour differs across countries. This thesis aims to contribute to the empirical literature by studying the effects of uncertainty on monetary policy in the developing country case of South Africa. In simplest terms, the thesis seeks to establish whether or not the South African Reserve Bank (SARB) responded optimally to uncertainty as suggested by theoretical models thereof. To this end, the thesis employs a theoretical model which resembles a structural rule-based approach. The optimal interest rate rule was derived given a set of structural equations relating to demand, the Phillips curve and the real exchange rate. To incorporate uncertainty, it is assumed that the coefficients are dependent on the variances of the exogenous variables, namely inflation, the output gap and the exchange rate. The uncertainty adjusted model allows us to investigate whether monetary policy is more aggressive or passive when uncertainty about the relevant exogenous variable increases. Inflation, output gap and exchange rate uncertainty estimates were derived through GARCH-model specifications related to the structural equations as defined in the theoretical model. The investigation considered both indirect and direct uncertainty effects with a sample period stretching from 1990 to 2011. The findings reported in this thesis provide strong evidence in support of the notion that uncertainty plays a significant role within the South African monetary policy landscape and contributes towards explaining the SARB’s actions. Furthermore, the results suggest that the SARB did in fact act optimally in responding more conservatively to target variable fluctuations on average. Also, the findings could potentially strengthen the case for inflation targeting as a monetary policy regime, as the results indicate a marked decline in the effects of uncertainty under inflation targeting than before. / Economics / D. Com. (Economics)

本研究使用相關係數隨時間變動的雙變量GARCH(1,1)模型(time-varying correlation bivariate GARCH(1,1) model)，討論台灣股票市場中，大公司與小公司之間的報酬、衝擊(shock)、波動(volatility)是否互為影響為主軸。其次，為了了解不同估計方法、相關係數的設定和解釋變數對結果造成的影響，亦設立了3種模型，作為本研究的比較模型。 本研究發現大公司與小公司過去的報酬，存在雙向的報酬外溢效果。換句話說，大公司與小公司過去的報酬分別都對「本身報酬」有影響外，對「對方的報酬」也有影響。進一步發現到：大公司過去受到的衝擊和波動不僅對本身的條件變異數造成影響，也影響到小公司的條件變異數。但相反地，小公司過去受到的衝擊和波動，只對本身的條件變異數有影響，對大公司的條件變異數沒有影響，所以大、小公司間的衝擊外溢效果和波動外溢效果有不對稱的現象。 從不同模型之比較也發現，在討論大公司與小公司的報酬及波動時，應重視兩者彼此相互影響的關係，在估計時使用多變量的方法，以捕捉彼此相依的條件共變異數及條件變異數之動態過程。除此之外，也應考量兩者的相關係數隨時間變動的特性，及過去的波動對描述對方條件變異數的重要性。 關鍵字：多變量、GARCH模型、波動性、外溢效果、不對稱性

本研究以天真避險、傳統OLS模型、OLS共整合模型及Bivariate GARCH模型探討SIMEX及OSE所交易的日經225 (Nikkei 225)股價指數期貨對日本及台灣股市風險的避險效果，測試在台灣股價指數期貨尚未推出之際，投資人是否可能採用鄰近國家，如日本的日經股價指數期貨，來規避台灣股市風險。本研究採用每週三週報酬資料，研究期間自1988年9月3日起至1995年12月底止，全部樣本期間共有376筆資料，劃分為兩個子期間，並以第二子期間做樣本外測試，避險期間分為一週、兩週及四週。 　　實證結果發現： 　　(1) SIMEX日經指數期約、OSE日經指數期約、日經股價指數及台灣股價指數的時間數列均非常態分配。經一階差分之後，上述四個時間數列才會為定態數列。日經股價指數期貨與日經股價指數之間有共整合關係，此乃表示現貨與期貨價格之間存在有長期均衡關係，但日經股價指數期貨與台灣股價指數之間並無共整合關係。 　　(2) Bivariate GARCH模式在各研究期間所得到的各參數的估計值，大多顯著，這說明不論在日本或台灣市場，以日經股價指數期貨規避股票市場風險時，期貨與現貨分配會有隨時間而變動的現象。 　　(3) 在日經指數的現貨市場中： 　　1. OLS共整合模型的避險比率較傳統OLS模型為高。使用SIMEX期貨契約避險所需要的避險比率較使用OSE期貨契約為避險工具時為小，而且不論使用SIMEX或OSE期貨契約避險，當避險期間越長，避險比率越大。 　　2. 在樣本內實證中，以OSE期貨契約避險所造成的投資組合變異數較使用SIMEX期約為大，而且投資組合變異數隨避險期間的增長而有下降的趨勢，但在樣本外的期間中，卻無如此的明顯趨勢。 　　3. 除了在日本股市大崩盤之前的實證期間顯示不論是使用SIMEX或OSE期貨契約，Bivariate GARCH模型的避險效果均較好之外，在其他的實證期間中，GARCH模型大約只比天真避險模式效果好，卻比其他模型效果差，而這種情況在使用OSE期貨契約時更為明顯，不過不論使用哪種模型，都能比不避險時減少大部份現貨的風險。 　　4. 從樣本內實證期間發現SIMEX與OSE契約在避險效果上是有差別的，但樣本外實證卻未發現避險效果上有明顯差別。 　　(4)在台灣股價指數的現貨市場下： 　　1. 不論使用SIMEX或OSE期貨契約避險在崩盤前所需要的避險比率均較崩盤後為高，而不論使用SIMEX或OSE期貨契約避險，避險比率均差不多。 　　2. 樣本內或樣本外實證都發現，若使用天真避險模式避險還不如不避險的好。除了在大崩盤後的樣本內實證中，GARCH模式的組合變異比傳統OLS模式為高之外，Bivariate GARCH模式的確優於其他避險模式。但日經指數期約與台灣股價指數所形成的投資組合變異數比在日本市場時高出甚多，且使用OLS或GARCH模式只能略微降低不避險狀態下所造成的變異數。不論是參數的估計值或避險績效都支持日經指數期貨與台灣股價指數間存在有GARCH效果。

隨著企業往全球化發展，產業環境也不斷的變遷，跨國購併已成為企業追求快速成長的手段之一，而近幾年新興國家的快速發展也使得開發中國家的企業逆向購併已開發國家企業的現象愈見普遍，因此，此議題特別值得加以關注，本研究欲針對中國和台灣的企業，探討在其在跨國購併上，是否能為公司股東創造價值。 本研究以2003年1月1日至2010年12月31日間，中國和台灣製造業之上市公司所從事的跨國購併交易案做為樣本，利用事件研究法及GARCH(1,1)的模型，對公司的股票報酬率進行衡量，檢測是否有顯著的異常報酬產生，並影響股東價值。 研究結果顯示，即使在購併宣告日之前，平均異常報酬率有顯著的正面效果，但在宣告日之後，卻轉而有顯著的負面效果，此一正一負正好抵消了購併預期應帶來的好處，因此當開發中國家的企業進行跨國購併時，對主併企業的股東價值並無顯著的正面影響。

Diss. Stockholm : Handelshögskolan, 2006 S. 1-9: introduction, s. 11-170: 5 research papers

Forecasting volatility with precision in financial market is very important. This paper examines the use of various forms of GARCH models for forecasting volatility. Three financial data sets from Japan (NIKKEI 225 index), the United States (Standard & Poor 500) and Germany (DAX index) are considered. A number of GARCH models, such as EGARCH, IGARCH, TGARCH, PGARCH and QGARCH models with normal distribution and student’s t distribution are used to fit the data sets and to forecast volatility. The Maximum Likelihood method and the Bayesian approach are used to estimate the parameters in the family of the GARCH models. The results show that the QGARCH model under student’s t distribution is the precise model for the NIKKEI 225 index in terms of fitting the data and forecasting volatility. The TGARCH under the student’s t distribution fits the S&P 500 index data better while the traditional GARCH model under the same distribution performs better in forecasting volatility. The PGARCH with student’s t distribution is the precise model for the DAX index in terms of fitting the data and forecasting volatility. / Department of Mathematical Sciences

Even though major advances in economic theory and modelling have in some cases furthered our understanding of how the economy works, the system as a whole has become more complex. If policymakers had perfect knowledge about the actual state of the economy, the various transmission mechanisms as well as the true underlying model, monetary intervention would be greatly simplified. In reality, however, the monetary authorities have to contend with considerable uncertainty in relation to the above-mentioned factors. This said, uncertainty has mostly been neglected in both the theoretical and empirical literature focusing on monetary policy analysis. Nonetheless, findings from a review of theoretical literature that does exist on this topic suggest that optimal central banks act more conservatively when faced with uncertainty. Similarly, empirical findings from the literature also favour conservatism. However, there is some evidence to suggest that this is not always the case. These results suggest that central banks do not always act optimally when faced with uncertainty. The limited number of industrial country cases examined prevents any generalised view from emerging. If anything, the literature findings suggest that central bank behaviour differs across countries. This thesis aims to contribute to the empirical literature by studying the effects of uncertainty on monetary policy in the developing country case of South Africa. In simplest terms, the thesis seeks to establish whether or not the South African Reserve Bank (SARB) responded optimally to uncertainty as suggested by theoretical models thereof. To this end, the thesis employs a theoretical model which resembles a structural rule-based approach. The optimal interest rate rule was derived given a set of structural equations relating to demand, the Phillips curve and the real exchange rate. To incorporate uncertainty, it is assumed that the coefficients are dependent on the variances of the exogenous variables, namely inflation, the output gap and the exchange rate. The uncertainty adjusted model allows us to investigate whether monetary policy is more aggressive or passive when uncertainty about the relevant exogenous variable increases. Inflation, output gap and exchange rate uncertainty estimates were derived through GARCH-model specifications related to the structural equations as defined in the theoretical model. The investigation considered both indirect and direct uncertainty effects with a sample period stretching from 1990 to 2011. The findings reported in this thesis provide strong evidence in support of the notion that uncertainty plays a significant role within the South African monetary policy landscape and contributes towards explaining the SARB’s actions. Furthermore, the results suggest that the SARB did in fact act optimally in responding more conservatively to target variable fluctuations on average. Also, the findings could potentially strengthen the case for inflation targeting as a monetary policy regime, as the results indicate a marked decline in the effects of uncertainty under inflation targeting than before. / Economics / D. Com. (Economics)

The GARCH model estimates the volatility of a time series. Information criteria are often used to determine orders of the GARCH model, although their suit- ability is not known. This thesis focuses on the order selection of the GARCH model using information criteria. The simulation study investigates whether in- formation criteria are appropriate for the model selection and how the selection depends on the order, number of observations, distribution of innovations, estima- tion method or model parameters. The predictive capabilities of models selected by information criteria are compared to the true model. 1

Text in English with summaries in English and Afrikaans / The introduction of single stock futures to a market presents the opportunity to assess an individual company's response to futures trading directly, in contrast to the market-wide impact obtained from index futures studies. Thirty-eight South African companies were evaluated in terms of a possible price, volume, and volatility effect due to the initial trading of their respective single stock futures contracts. An event study revealed that SSF trading had little impact on the underlying share prices. A normalised volume comparison pre to post SSF trading showed a general increase in spot market trading volumes. The volatility effect was the main focus of this study with a GARCH(1,1) model establishing a volatility structure (pattern of behaviour) per company. Results showed a reduction in the level and changes in the structure of spot market volatility. In addition, a dummy variable regression could find no evidence of an altered company-market relationship (systematic risk) post futures. / Business Management / M.Com. (Business Management)

Thesis (MComm)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Accurate estimation of Value at Risk (VaR) and Expected Shortfall (ES) is critical in the management of extreme market risks. These risks occur with small probability, but the financial impacts could be large. Traditional models to estimate VaR and ES are investigated. Following usual practice, 99% 10 day VaR and ES measures are calculated. A comprehensive theoretical background is first provided and then the models are applied to the Africa Financials Index from 29/01/1996 to 30/04/2013. The models considered include independent, identically distributed (i.i.d.) models and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) stochastic volatility models. Extreme Value Theory (EVT) models that focus especially on extreme market returns are also investigated. For this, the Peaks Over Threshold (POT) approach to EVT is followed. For the calculation of VaR, various scaling methods from one day to ten days are considered and their performance evaluated. The GARCH models fail to converge during periods of extreme returns. During these periods, EVT forecast results may be used. As a novel approach, this study considers the augmentation of the GARCH models with EVT forecasts. The two-step procedure of pre-filtering with a GARCH model and then applying EVT, as suggested by McNeil (1999), is also investigated. This study identifies some of the practical issues in model fitting. It is shown that no single forecasting model is universally optimal and the choice will depend on the nature of the data. For this data series, the best approach was to augment the GARCH stochastic volatility models with EVT forecasts during periods where the first do not converge. Model performance is judged by the actual number of VaR and ES violations compared to the expected number. The expected number is taken as the number of return observations over the entire sample period, multiplied by 0.01 for 99% VaR and ES calculations. / AFRIKAANSE OPSOMMING: Akkurate beraming van Waarde op Risiko (Value at Risk) en Verwagte Tekort (Expected Shortfall) is krities vir die bestuur van ekstreme mark risiko’s. Hierdie risiko’s kom met klein waarskynlikheid voor, maar die finansiële impakte is potensieel groot. Tradisionele modelle om Waarde op Risiko en Verwagte Tekort te beraam, word ondersoek. In ooreenstemming met die algemene praktyk, word 99% 10 dag maatstawwe bereken. ‘n Omvattende teoretiese agtergrond word eers gegee en daarna word die modelle toegepas op die Africa Financials Index vanaf 29/01/1996 tot 30/04/2013. Die modelle wat oorweeg word sluit onafhanklike, identies verdeelde modelle en Veralgemeende Auto-regressiewe Voorwaardelike Heteroskedastiese (GARCH) stogastiese volatiliteitsmodelle in. Ekstreemwaarde Teorie modelle, wat spesifiek op ekstreme mark opbrengste fokus, word ook ondersoek. In hierdie verband word die Peaks Over Threshold (POT) benadering tot Ekstreemwaarde Teorie gevolg. Vir die berekening van Waarde op Risiko word verskillende skaleringsmetodes van een dag na tien dae oorweeg en die prestasie van elk word ge-evalueer. Die GARCH modelle konvergeer nie gedurende tydperke van ekstreme opbrengste nie. Gedurende hierdie tydperke, kan Ekstreemwaarde Teorie modelle gebruik word. As ‘n nuwe benadering oorweeg hierdie studie die aanvulling van die GARCH modelle met Ekstreemwaarde Teorie vooruitskattings. Die sogenaamde twee-stap prosedure wat voor-af filtrering met ‘n GARCH model behels, gevolg deur die toepassing van Ekstreemwaarde Teorie (soos voorgestel deur McNeil, 1999), word ook ondersoek. Hierdie studie identifiseer sommige van die praktiese probleme in model passing. Daar word gewys dat geen enkele vooruistkattingsmodel universeel optimaal is nie en die keuse van die model hang af van die aard van die data. Die beste benadering vir die data reeks wat in hierdie studie gebruik word, was om die GARCH stogastiese volatiliteitsmodelle met Ekstreemwaarde Teorie vooruitskattings aan te vul waar die voorafgenoemde nie konvergeer nie. Die prestasie van die modelle word beoordeel deur die werklike aantal Waarde op Risiko en Verwagte Tekort oortredings met die verwagte aantal te vergelyk. Die verwagte aantal word geneem as die aantal obrengste waargeneem oor die hele steekproefperiode, vermenigvuldig met 0.01 vir die 99% Waarde op Risiko en Verwagte Tekort berekeninge.