This thesis describes statistical approaches of investment portfolio constructions. The theoretic part presents modern portfolio theory and specific statistical methods used to estimate expected revenue and risk of portfolio. These procedures are specifically selection method, modelling volatility using multivariate GARCH model, primarily DCC GARCH procedure and Bayes approach with Jeffrey's and conjugated density. The practical part of the thesis covers application of above mentioned statistical methods of investment portfolio constructions. The maximization of Sharp's ratio was chosen as optimization task. Researched portfolios are created from Austria Traded Index issues of shares where suitable time series of historical daily closed prices. Results attained within assembled portfolios in two year investment interval are later compared.

This diploma thesis is devoted to the linkages among stock, bond and foreign exchange markets in the Czech Republic, Austria, Germany and Poland during the period from the beginning of the year 2007 to the end of the year 2014. In order to complexly describe the interconnections among the markets, we utilized two kinds of spillover indices (from the generalized and structural VAR model), dynamic correlation coefficients obtained from the multivariate GARCH model and contemporaneous coefficients from the structural VAR model that was identified through heteroskedasticity in structural shocks. These methods enabled us to describe the linkages among the markets from different angles, to capture their time evolution and to obtain a notion about the transmission mechanism among these markets in Central Europe. The results, inter alia, indicate an intensifying interconnection among the markets during crisis periods, lowering impact of stock markets, increasing influence of bonds and a dominant role of German bonds and Austrian stocks. At the same time, we were able to capture the influence of the European sovereign debt crisis on the spillovers and on the intensity of linkages among the markets. We showed that the intensity of linkages among bond markets relented, probably as a result of higher emphasis on the...

Most of the notations and terminological conventions used in this thesis are Statistical. The aim in risk management is to describe the risk factors present in time series. In order to group these risk factors, one needs to distinguish between different stochastic processes and put them into different classes. The risk factors discussed in this thesis are fat tails and mean reversion. The presence of these risk factors fist need to be found in the historical dataset. I will refer to the historical dataset as the original dataset. The Ljung- Box-Pierce test will be used in this thesis to determine if the distribution of the original dataset has mean reversion or no mean reversion. / Mathematical Sciences / M.Sc. (Applied Mathematics)

本研究目的在於探討韓國、巴西與俄羅斯等實施外匯管制的國家，其上市本國貨幣匯率期貨對該國外匯市場之影響。及小型開放經濟的紐西蘭，在CME上市的美元/紐幣匯率期貨後，對該國外匯市場之影響。以加入虛擬變數單變量GARCH模型探討匯率期貨成立期間對匯率現貨的波動性是否會產生影響；以雙變量GARCH模型探討匯率期貨波動是否會對匯率現貨波動造成影響。 研究期間乃以各國引入匯率期貨契約的基準日之下，前後各兩年的匯率日報酬率資料。實證結果顯示： 一、韓國、巴西與俄羅斯，其開放匯率期貨交易後反而會降地現貨市場的波動，但小型開放經濟的紐西蘭，在CME上市的美元/紐幣匯率期貨後，會增加現貨市場的波動。 二、以上四個國家其外匯現貨市場的波動並不會受外匯期貨市場波動的影響。 / The objective of this study is to evaluate the impact upon foreign exchange markets for exchange control countries as Korea, Brazil, and Russia when foreign exchange futures was introduced, and small-scale open economy as New Zealand when foreign exchange futures was introduced in CME. This study was an application of univariate and bivariate GARCH models to investigate the effect of foreign exchange futures trading and volatility on spot market volatility. This study utilized the daily foreign exchange rate return series based on foreign exchange futures introduced with the former and latter two years. The empirical results are as follows: 1. The spot volatility decreases significantly after foreign exchange futures trading in Korea, Brazil, and Russia. The spot volatility increases significantly after foreign exchange futures trading in New Zealand. 2. The futures volatility does not affect the spot volatility in Korea, Brazil, Russia, and New Zealand.

This report is for MA575: Market and Credit Risk Models and Management, given by Professor Marcel Blais. In this project, three different methods for estimating Value at Risk (VaR) and Expected Shortfall (ES) are used, examined, and compared to gain insightful information about the strength and weakness of each method. In the first part of this project, a portfolio of underlying assets and vanilla options were formed in an Interactive Broker paper trading account. Value at Risk was calculated and updated weekly to measure the risk of the entire portfolio. In the second part of this project, Value at Risk was calculated using semi-parametric model. Then the weekly losses of the stock portfolio and the daily losses of the entire portfolio were both fitted into ARMA(1,1)-GARCH(1,1), and the estimated parameters were used to find their conditional value at risks (CVaR) and the conditional expected shortfalls (CES).

Su, Yiwen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (p. 76-84). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.9 / Chapter 2.1 --- Hedge Ratio Review --- p.9 / Chapter 2.2 --- Estimating the Hedge Ratio --- p.13 / Chapter 2.2.1 --- Static Hedge Ratio --- p.13 / Chapter 2.2.2 --- "Dynamic Hedge Ratio, Multivariate GARCH Frame-work and DCC Model" --- p.14 / Chapter 3 --- Futures Market Efficiency --- p.19 / Chapter 3.1 --- Market Efficiency and Cointegration Test --- p.20 / Chapter 4 --- Model Specifications and Hedging Strategy --- p.24 / Chapter 4.1 --- Model Specifications --- p.24 / Chapter 4.1.1 --- BGARCH-DCC Model --- p.25 / Chapter 4.1.2 --- Symmetric BGARCH-DCC Model --- p.28 / Chapter 4.1.3 --- Asymmetric BGARCH-DCC Model --- p.31 / Chapter 4.2 --- Hedge Ratio --- p.33 / Chapter 4.2.1 --- MV Hedge Ratio --- p.34 / Chapter 4.2.2 --- Zero-VaR Hedge Ratio --- p.35 / Chapter 4.3 --- Evaluation of Hedge Effectiveness --- p.38 / Chapter 5 --- Data Description and Empirical Results --- p.39 / Chapter 5.1 --- Preliminary Data Analysis --- p.39 / Chapter 5.2 --- Estimation Results --- p.42 / Chapter 5.3 --- Dynamic Hedging Performance --- p.53 / Chapter 6 --- Conclusion --- p.68 / Chapter A --- Equation Derivation --- p.72 / Bibliography --- p.76

abstract: 中国商品期货市场经历30年发展，已初备协调资源分配、对冲经营风险的功能。但受产业自身和期货市场发展的制约，各期货品种市场有效性参差不齐。随着我国经济从增量阶段过渡到存量阶段，期货作为企业的价格管理和风险控制工具的重要性日益凸显，因此研究我国商品期货市场有效性具有非常好的现实意义。 本文开创性的从期货的基本功能——资源配置的角度出发，提出有效市场是指其期货价格能够对本行业社会资源起到合理的调配作用的市场。在内容安排上，本文首先总结了现有国际成熟期货品种的特点并找出能够反映期货对资源配置能力的四个指标假说，分别为期现回归性、利润波动性、库存波动性以及现金流变化，然后通过数学模型证明指标数据和品种成熟度的关联，最后应用该套指标对我国商品市场有效性进行检验。数学方法上，本文先采用Bai-Perron内生多重结构突变模型对时间序列进行突变点检验，然后对断点时间序列分别进行多元回归，并在剔除季节性和周期性后，通过平稳性检验、ARCH效应检验结果来确定相应的Garch模型，并用Garch模型来描述时间序列的波动性。 通过数学验证，我们认为期现回归性、利润波动性、库存波动性以及现金流变化这四个指标可以作为反映期货成熟度的检验指标，用该套方法对国内部分活跃品种检验后发现大连豆粕期货已经具备成熟品种的特征，本文认为豆粕期货市场是有效的；PTA、玉米淀粉期货的四个检验指标在近年来表现出时间序列优化的特点，但因时间较短尚不稳定，可以认为是接近成熟的品种；而螺纹钢和铝期货在多数指标上表现不佳，表明他们对社会资源配置能力较差，因此本文认为螺纹钢和铝期货市场是活跃但非有效的。通过进一步分析，本文认为品种的期现回归性差是制约其资源配置能力发挥的关键因素，而交易标的不明确、 仓单制作难度大、产业参与度低以及期货设计中的其他限制因素又是导致期现回归性差的重要原因。 / Dissertation/Thesis / Doctoral Dissertation Business Administration 2019

This dissertation investigates the volatility of the relationships between exchange rates and interest rates. The first part of the paper explores the transmission relationship between these two markets using a time-series model. Previous studies have assumed that covariance was constant in both markets. However, if the volatilities of the exchange rate and interest rate markets are correlated over time, the interaction and spillover effects between the two markets may be affected by time-varying covariance. Hence, this paper utilizes the BEKK-GARCH model developed by Engle and Kroner (1995) to capture the dynamic relationship between the exchange rates and interest rates. This study uses the returns data for G7 members¡¦ exchange rates and interest rates to test whether these markets exhibited volatilities spillover from 1978 to 2009. The results show bi-directional volatility spillovers in the markets of the UK, the Euro countries, and Canada, where the volatilities of the two markets were interrelated. The second part of the paper explores the relationship between exchange rates and interest rates using a jump diffusion model. Previous studies assumed that the dynamic processes of exchange rates and interest rates follow a diffusion process with a continuous time path, but an increasing number of empirical studies have shown that a continuous diffusion stochastic model does not capture the dynamic process of these variables. Thus, this paper investigates the discontinuous variables of exchange rates and interest rates and assumes that these variables follow a jump diffusion process. The UIRP model is employed to explore the relationship between both variables and to divide the systematic risk into systematic continuous risk and systematic jump risk. The returns data for G7 members¡¦ exchange rates and interest rates from 2005 to 2010 were analyzed to test whether the expected exchange rate is affected by jump components when the interest rate market experiences a jump. The results show that the jump diffusion model has more explanatory power than the pure diffusion model does, and, when the interest rate market experiences a jump risk, the systematic jump risk has a significant relationship with the expected exchange rates in some G7 countries.

The objective of this dissertation is to model the volatility of financial time series data using ARCH, GARCH and stochastic volatility models. It is found that the ARCH and GARCH models are easy to fit compared to the stochastic volatility models which present problems with respect to the distributional assumptions that need to be made. For this reason the ARCH and GARCH models remain more widely used than the stochastic volatility models. The ARCH, GARCH and stochastic volatility models are fitted to four data sets consisting of daily closing prices of gold mining companies listed on the Johannesburg stock exchange. The companies are Anglo Gold Ashanti Ltd, DRD Gold Ltd, Gold Fields Ltd and Harmony Gold Mining Company Ltd. The best fitting ARCH and GARCH models are identified along with the best error distribution and then diagnostics are performed to ensure adequacy of the models. It was found throughout that the student-t distribution was the best error distribution to use for each data set. The results from the stochastic volatility models were in agreement with those obtained from the ARCH and GARCH models. The stochastic volatility models are, however, restricted to the form of an AR(1) process due to the complexities involved in fitting higher order models. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2011.

Most of the notations and terminological conventions used in this thesis are Statistical. The aim in risk management is to describe the risk factors present in time series. In order to group these risk factors, one needs to distinguish between different stochastic processes and put them into different classes. The risk factors discussed in this thesis are fat tails and mean reversion. The presence of these risk factors fist need to be found in the historical dataset. I will refer to the historical dataset as the original dataset. The Ljung- Box-Pierce test will be used in this thesis to determine if the distribution of the original dataset has mean reversion or no mean reversion. / Mathematical Sciences / M.Sc. (Applied Mathematics)