Orientador: Luiz Koodi Hotta / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-23T04:22:11Z (GMT). No. of bitstreams: 1 Almeida_Danielde_M.pdf: 17481253 bytes, checksum: 669620c3fe4155707f86370dd1778d01 (MD5) Previous issue date: 2013 / Resumo: O objetivo da dissertação é estudar modelos de volatilidade que consideram dois tipos de assimetria usualmente encontradas em séries de finanças, a assimetria das perturbações e o efeito de alavancagem. Perturbações assimétricas são utilizadas devido ao fato estilizado de que perdas têm distribuição com cauda mais pesada do que ganhos. Já o efeito de alavancagem leva em consideração que perdas têm maior influência na volatilidade do que os ganhos. São estudados os modelos GARCH univariados que contemplam os dois tipos de assimetria separadamente e conjuntamente e modelos GARCH multivariados que permitem o efeito de alavancagem. Os resultados são apresentados em dois artigos. O primeiro descreve os principais modelos univariados que possam explicar estes dois fatos estilizados e analisa, com detalhes, oito séries: os índices Ibovespa, Merval e S&P 500, e as ações Itaú-Unibanco, Vale, Petrobras, Banco do Brasil e do Bradesco. A conclusão é que os dois tipos de assimetria estão presentes nas séries, na maioria das vezes simultaneamente. O segundo artigo faz uma revisão dos principais modelos multivariados da família GARCH, incluindo modelos com efeitos assimétricos nas variâncias e nas covariâncias condicionais. Alguns destes modelos são analisados com mais detalhes através de simulações. Considerou-se as perdas de eficiência na estimativa da matriz de volatilidade ao se ter erros de especificação, isto é ajustar um determinado modelo a séries geradas por outros modelos. Os modelo mais utilizados na literatura são aplicados a uma série trivariada, contendo o índice Ibovespa e as ações Petrobras e Vale. Os três modelos selecionados pelos critérios AIC e BIC, possuem o efeito de alavancagem / Abstract: The objective of this dissertation is to study volatility models that consider two types of asymmetry usually found in finance series, the skewness of the innovations and the leverage effect. Skewness means that the distribution of losses has a heavier tail than the distribution of gains. The leverage effect stems from the fact that losses have a greater influence on future volatilities than gains. It is considered univariate GARCH models that include both types of asymmetry, separately and jointly, and multivariate GARCH models that allow for leverage effects. The results are presented in two papers. The first one describes the main univariate models that consider these two stylized facts and analyzes, in detail, eight series: the Ibovespa, Nasdaq and S&P 500 indices, and the Itaú-Unibanco, Vale, Petrobras, Banco do Brasil and Bradesco stocks. The conclusion is that both stylized facts are present in some series, mostly simultaneously. The second paper reviews the main multivariate GARCH models, including models with asymmetric effects on conditional variances and covariance. Some of these models are analyzed in more detail through simulations. The most used models in the literature are applied to a three-dimensional time series, containing the Bovespa index and the Petrobras and Vale markets. The three models selected by AIC and BIC criteria allow for leverage effects / Mestrado / Estatistica / Mestre em Estatística

自從2008年金融危機爆發後，黑天鵝事件相繼出現，VIX成為投資人衡量股市波動度的重要指標。但是若投資人想使用VIX避險，僅能透過限專業投資人參與的VIX期貨。而在近年ETF產品盛行的背景下，投資標的更加多元的交易所交易債券（ETN）也應運而生，使一般投資人得以進入以往難以觸及或交易成本高昂的市場。本研究採用兩檔交易量較大之VIX ETN，分別追蹤VIX短期與中期期貨指數之VXX與VXZ，希望透過建構GARCH模型用以預測其隔日價格，並以此預測的價格近一步建構避險策略，目標係在預期空頭即將發生時，提供投資人除了VIX期貨和波動相對平穩的債券以外的避險替代工具。 建構GARCH模型的部分，本研究主要參考Kambouroudis和McMillan（2013）的文獻，在變異數方程式中加入輔助變數，可以增加模型的預測能力，故本研究在VIX ETN之GARCH模型的變異數方程式中加入VIX、短期VIX指數及中期VIX指數。實證結果顯示，在VIX ETN的GARCH模型中同時加入VIX相關指數，確實能提高配適程度並增進預測能力，尤其當加入的輔助變數與VIX ETN追蹤標的的到期期限相符時，此改善模型的效果最為顯著。 本研究接者參考Alexander和Korovilas（2012）的VIX ETN避險研究，文獻顯示，在S&P 500 ETF投資組合中加入VXX與VXZ避險可提高夏普比率。本研究在此基礎上，額外考量了不同的持有期間、進場條件、股債混合的投資組合，並分別比較兩種ETN的避險效果。本研究發現只在VIX大於20時才進場建構避險部位的策略，提前買入VIX ETN確實可以做為良好的避險工具。此外，在此策略下，VIX ETN亦則可達到比持有債券更佳的避險效果。而本研究所測試的兩種VIX ETN中，又以VXX 避險效果更佳，因VXX乃是追蹤VIX短期期貨指數，更能反映市場短期的變化，搭配滾動的避險比率，能更加精準的反應空頭時期劇烈的波動。 / Since the 2008 financial crisis, along with the black swan events, the volatility of global stock market has intensified, and VIX index becomes an important indicator for investors to measure the volatility of the stock market. However, if investors would like to use VIX index for hedge, they could only use VIX futures, which is only for professional investors to participate. In recent years, the prevalence and popularity of the various ETPs lead to the booming of VIX ETNs, which has become an alternative for regular investors to invest in VIX index. Therefore, this study hopes to build GARCH model for VIX ETN and predict their prices of the next day, and use the prediction to build hedging strategies. In this paper, this study mainly refers to the paper of Kambouroudis and McMillan (2013) to construct the VXX and VXZ prediction models. Because the two VIX ETNs track the S&P 500 VIX short-term and medium-term futures index respectively, the study add the VIX index, short-term VIX index and medium-term VIX index in the GARCH models. The empirical results show that the addition of VIX and other relevant VIX indices in the VIX ETN GARCH models can improve the forecasting ability. In particular, when the maturity of the VIX index is consistent with the maturity of the VIX ETN’s tracking target, it would improve the prediction power the most. Based on the predicted VIX ETN prices, this study then constructs the hedging strategies, considering the different holding period, the entry condition and the stock and debt mixed portfolio, and also compares the hedging effect of VXX and VXZ respectively. This study found that under the strategy that only enter the VIX ETN market when VIX was greater than 20, VIX ETN can indeed be a good hedge tool and reduce the standard deviation of the portfolio. In addition, under this strategy, if investors use VIX ETN to hedge, investors can achieve a higher return and lower standard deviation than holding a bond to hedge. Finally, among the two VIX ETNs tested in this study, VXX is a better hedge tool against VXX. It is because VXX tracks the VIX short-term futures index which reflects the short-term changes in the market and hence could reflect the short-term volatility better.

This thesis aims to construct an optimal portfolio and model as well as forecast its volatility. The performance of the optimal portfolio is then compared to two benchmarks, namely, an equally weighted portfolio and the market index SP 500. The volatility is estimated by employing two GARCH-type models known as standard GARCH, and GJR-GARCH. The GJR-GARCH outperformed its counterpart in terms of Log-likelihood, AIC, and BIC. The forecast performance is compared based on two statistical errors, root mean squared error, and mean absolute error. The optimal portfolio outperformed its counterparts in both statistical errors. Moreover, standard GARCH gave lower statistics than GJR-GARCH. These empirical results are of important significance to portfolio management and risk management processes.

This thesis examines the volatility forecasting performance of six commonly used forecasting models; the simple moving average, the exponentially weighted moving average, the ARCH model, the GARCH model, the EGARCH model and the GJR-GARCH model. The dataset used in this report are three different Nordic equity indices, OMXS30, OMXC20 and OMXH25. The objective of this paper is to compare the volatility models in terms of the in-sample and out-of-sample fit. The results were very mixed. In terms of the in-sample fit, the result was clear and unequivocally implied that assuming a heavier tailed error distribution than the normal distribution and modeling the conditional mean significantly improves the fit. Moreover a main conclusion is that yes, the more complex models do provide a better in-sample fit than the more parsimonious models. However in terms of the out-of-sample forecasting performance the result was inconclusive. There is not a single volatility model that is preferred based on all the loss functions. An important finding is however not only that the ranking differs when using different loss functions but how dramatically it can differ. This illuminates the importance of choosing an adequate loss function for the intended purpose of the forecast. Moreover it is not necessarily the model with the best in-sample fit that produces the best out-of-sample forecast. Since the out-of-sample forecast performance is so vital to the objective of the analysis one can question whether the in-sample fit should even be used at all to support the choice of a specific volatility model.

In this study we analyse the relationship between renewable energy, electricity prices, and the stock market. The impact from electricity prices on stock markets have previously been thoroughly analysed. However, our study evaluates if a country’s share of renewable energy in their electricity production impacts the strength and size of the relationship in question. We use data from eight countries of rather equal economical sizes but that uses very opposed energy sources. Sweden, Norway, Finland, and Latvia represent countries with high amounts of renewable energy. While Belgium, Netherlands, Poland, and Hungary constitute countries with low shares of renewable energy. By using daily data between January 2016 and December 2021, we aim to understand the relationship of electricity prices and stock market indices and the role of renewable energy in this relationship. We do this by using Johansen’s cointegration test as well as analysing the correlation between volatilities through a DCC-GARCH(1,1). We find that both tests indicate a negative correlation between the electricity and stock markets as well as for their volatilities. In addition, we find some disparities between countries depending on their share of renewable energy. The impact of electricity prices on the stock market tends to be more pronounced for countries that use larger shares of renewable energy. Finally, findings suggest that the energy source used for electricity production also constitute an important factor in the connectivity of the markets. Wind power was found to be the main cause to the larger fluctuations on the electricity market leading to stronger relationship to the stock market. While hydro power is the more stable option of renewable energy with smaller variances and large storage capacity, weakening the link between the electricity market and stock market.

Changing in variance or volatility with time can be modeled as deterministic by using autoregressive conditional heteroscedastic (ARCH) type models, or as stochastic by using stochastic volatility (SV) models. This study compares these two kinds of models which are estimated on Turkish / USA exchange rate data. First, a GARCH(1,1) model is fitted to the data by using the package E-views and then a Bayesian estimation procedure is used for estimating an appropriate SV model with the help of Ox code. In order to compare these models, the LR test statistic calculated for non-nested hypotheses is obtained.

The purpose of this thesis is to investigate the financial volatility dynamics through the GARCH modelling framework. We use univariate and multivariate GARCH-type models enriched with long memory, asymmetries and power transformations. We study the financial time series volatility and co-volatility taking into account the structural breaks detected and focusing on the effects of the corresponding financial crisis events. We conclude to provide a complete framework for the analysis of volatility with major policy implications and benefits for the current risk management practices. We first investigate the volume-volatility link for different investor categories and orders, around the Asian crisis applying a univariate dual long memory model. Our analysis suggests that the behaviour of volatility depends upon volume, but also that the nature of this dependence varies with time and the source of volume. We further apply the vector AR-DCC-FIAPARCH and the UEDCC-AGARCH models to several stock indices daily returns, taking into account the structural breaks of the time series linked to major economic events including crisis shocks We find significant cross effects, time-varying shock and volatility spillovers, time-varying persistence in the conditional variances, as well as long range volatility dependence, asymmetric volatility response to positive and negative shocks and the power of returns that best fits the volatility pattern. We observe higher dynamic correlations of the stock markets after a crisis event, which means increased contagion effects between the markets, a continuous herding investors’ behaviour, as the in-crisis correlations remain high, and a higher level of correlations during the recent financial crisis than during the Asian. Finally, we study the High-frEquency-bAsed VolatilitY (HEAVY) models that combine daily returns with realised volatility. We enrich the HEAVY equations through the HYAPARCH formulation to propose the HYDAP-HEAVY (HYperbolic Double Asymmetric Power) and provide a complete framework to analyse the volatility process.

For the purpose of modelling and prediction of volatility, the family of Stochastic Volatility (SV) models is an alternative to the extensively used ARCH type models. SV models differ in their assumption that volatility itself follows a latent stochastic process. This reformulation of the volatility process makes however model estimation distinctly more complicated for the SV type models, which in this paper is conducted through Markov Chain Monte Carlo methods. The aim of this paper is to assess the standard SV model and the SV model assuming t-distributed errors and compare the results with their corresponding GARCH(1,1) counterpart. The data examined cover daily closing prices of the Swedish stock index OMXS30 for the period 2010-01-05 to 2016- 03-02. The evaluation show that both SV models outperform the two GARCH(1,1) models, where the SV model with assumed t-distributed error distribution give the smallest forecast errors.

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There is a large body of research that indicates that international equity markets co-move over time. This co-movement manifests in various instruments, ranging from equities and bonds to soft commodities. However, this co-movement is more prevalent over crisis periods and can be seen in returns and volatility transmission effects. The recent financial crisis demonstrated that no local market is immune to transmission effects from international markets. South African financial market participants, such as investors and policymakers, have a vested interest in understanding how the equity market in particular and the economy in general react to international financial crises. This study aims to contribute an improved understanding of how the South African equity market interacts with international equity markets, by identifying the degree of price and volatility transmission before, during, and after an international financial crisis. This was done by investigating the possibility of changes in price and volatility transmissions from the Asian financial crisis (1997–1998), the dotcom bubble (2000–2001) and the more recent subprime financial crisis (2007–2009). An Exponential Generalized Autoregressive Conditional Heteroskedasticity (E-GARCH) model was employed within the framework of an Aggregate Shock model. The results indicate that during the international financial crises studied, the JSE All Share Index was directly affected through contagion effects inherent in the returns of the originating crisis country. Volatility transmissions during international financial crises came directly from the originating crisis country. Finally, the FTSE 100 Index was the main exporter of price and volatility transmission to the JSE All Share Index. / Thesis (M.Com. (Risk management))--North-West University, Potchefstroom Campus, 2012