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This article discusses a comparison of the GARCH and EGARCH conditional variance methods, with respect to the Fuzzy Gaussian GARCH and Fuzzy Gaussian EGARCH. The returns of four exchange rates were forecasted at daily periodicity from January 2015 to November 2022 and out-of-sample, January 2019, and December 2022. The results indicate that the Fuzzy GARCH and Fuzzy EGARCH models better estimate the volatility behaviour of the exchange market series compared to traditional techniques. Therefore, the recommendation is to estimate other high volatility variables to verify the efficiency of the fuzzy techniques, however, the main limitation is that it is not possible to apply traditional econometric tests for fuzzy techniques because the parameters are not estimated with the logarithm of maximum likelihood. The estimation of the parameters of GARCH and EGARCH models with fuzzy theory is the originality proposal. In conclusion, fuzzy methodologies have less error in forecasting the volatility of in-sample and out-of-sample exchange rates., El presente artículo compara los métodos de varianza condicional GARCH y EGARCH, con respecto a la propuesta Fuzzy Gaussian GARCH y Fuzzy Gaussian EGARCH. Se pronosticó la rentabilidad de cuatro tipos de cambio en periodicidad diaria desde enero 2015 a noviembre 2022 y fuera de muestra, enero 2019 y diciembre 2022. Los resultados revelan que los modelos Fuzzy GARCH y Fuzzy EGARCH estiman mejor el comportamiento de la volatilidad de las series del mercado cambiario en comparación con las técnicas tradicionales. Por lo que, la recomendación es estimar otras variables de alta volatilidad para verificar la eficiencia de las técnicas difusas, sin embargo, la principal limitación es que no es posible aplicar las pruebas econométricas tradicionales para técnicas difusas porque los parámetros no son estimados con el logaritmo de máxima verosimilitud. La estimación de los parámetros de los modelos GARCH y EGARCH con teoría difusa es la propuesta de originalidad. En conclusión, las metodologías difusas tienen menos error al pronosticar la volatilidad de los tipos de cambio dentro muestra y fuera de muestra.

Over the period 1980-2022, we examined the transmission effect of oil prices on Nigeria's exchange rate. E-GARCH (Exponential GARCH) model is employed in this study. We used Augmented Dickey Fuller to determine a unit root, integrating exchange rates, crude oil prices, external reserves, GDP, inflation, and interest rates to one I(1) and zero I(0). We used Johansen Co-integration to determine long-term relationships. Interest rates, inflation, and crude oil prices all correlated positively with each other. A statistically insignificant result is shown by the variance equation, indicating there is no correlation between crude oil prices and exchange rates. The Nigerian exchange rate is not affected by volatility transmission or leverage due to fluctuations in crude oil prices. According to the study, governments should take monetary policy measures to stabilize exchange rates during unpredictable oil price fluctuations. It is necessary to adjust the naira exchange rate when oil prices fluctuate.

Over the period 1980-2022, we examined the transmission effect of oil prices on Nigeria's exchange rate. E-GARCH (Exponential GARCH) model is employed in this study. We used Augmented Dickey Fuller to determine a unit root, integrating exchange rates, crude oil prices, external reserves, GDP, inflation, and interest rates to one I(1) and zero I(0). We used Johansen Co-integration to determine long-term relationships. Interest rates, inflation, and crude oil prices all correlated positively with each other. A statistically insignificant result is shown by the variance equation, indicating there is no correlation between crude oil prices and exchange rates. The Nigerian exchange rate is not affected by volatility transmission or leverage due to fluctuations in crude oil prices. According to the study, governments should take monetary policy measures to stabilize exchange rates during unpredictable oil price fluctuations. It is necessary to adjust the naira exchange rate when oil prices fluctuate.

By detailing the volatility response to shocks in several Asian nations, a dimension that has not been examined in the existing literature, our study contributes to the body of literature. The empirical data from the study indicate that volatility displayed asymmetric behavior in a few select Asian stock markets over the study period. In relation to this study, we saw that the volatility reaction followed a consistent pattern in the Asian region. For all but a few select markets, shocks are homogeneous in size and sign.  Additionally, there is evidence that volatility responses are persistent across all Asian stock markets, which suggests that the impact of volatility will gradually diminish. This study offers helpful information to the investor community to help them make informed decisions about their investments.

By detailing the volatility response to shocks in several Asian nations, a dimension that has not been examined in the existing literature, our study contributes to the body of literature. The empirical data from the study indicate that volatility displayed asymmetric behavior in a few select Asian stock markets over the study period. In relation to this study, we saw that the volatility reaction followed a consistent pattern in the Asian region. For all but a few select markets, shocks are homogeneous in size and sign.  Additionally, there is evidence that volatility responses are persistent across all Asian stock markets, which suggests that the impact of volatility will gradually diminish. This study offers helpful information to the investor community to help them make informed decisions about their investments.

This study empirically examined the asymmetric oil price shocks in Nigeria from 1981q1-2019q4 using the Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model. The EGARCH model was employed to investigate the asymmetric oil price shocks by obtaining the conditional variance from the estimated results. Empirical results revealed a weak indication for leverage effect and a strong indication for asymmetric effect. The positive egarch (L2) coefficient means that unanticipated increases in the price crude Oil are more profitable than unanticipated decreases in the price of crude Oil. Also, the results revealed strong asymmetry of oil price shocks in Nigeria. In specific terms, the positive asymmetric coefficient (1.8276) means an observed tendency of the crude oil price shock to be higher by approximately 1.83 per cent in declining oil prices in the crude oil market than in rising prices in the oil markets. Based on the above, the study recommended appropriate export diversification policies to reduce the dependency on crude oil exports as the major export (revenue) in the economy. This will offset crude oil price shocks such as the COVID-19 pandemic shock on Oil price, especially from an unanticipated decrease in crude oil prices in the international market. Key Words: Oil price, Oil Price Shocks, Asymmetry, EGARCH, Nigeria

This study empirically examined the asymmetric oil price shocks in Nigeria from 1981q1-2019q4 using the Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model. The EGARCH model was employed to investigate the asymmetric oil price shocks by obtaining the conditional variance from the estimated results. Empirical results revealed a weak indication for leverage effect and a strong indication for asymmetric effect. The positive egarch (L2) coefficient means that unanticipated increases in the price crude Oil are more profitable than unanticipated decreases in the price of crude Oil. Also, the results revealed strong asymmetry of oil price shocks in Nigeria. In specific terms, the positive asymmetric coefficient (1.8276) means an observed tendency of the crude oil price shock to be higher by approximately 1.83 per cent in declining oil prices in the crude oil market than in rising prices in the oil markets. Based on the above, the study recommended appropriate export diversification policies to reduce the dependency on crude oil exports as the major export (revenue) in the economy. This will offset crude oil price shocks such as the COVID-19 pandemic shock on Oil price, especially from an unanticipated decrease in crude oil prices in the international market. Key Words: Oil price, Oil Price Shocks, Asymmetry, EGARCH, Nigeria

Covid19 hit the world’s financial markets by surprise in March 2020 and ensuing volatility marked an end to the prior low-volatility environment. This Black Swan engendered numerous publications establishing how the equity market responded to the exogenous shock. However, there is no applicable comparison to Nasdaq100 regarding how models perform during extreme conditions such as ante, amid and post Covid19. Furthermore, goodness of fit together with forecasting accuracy are further examined in the light of new intra-day data from Oxford Man Institute covering this time-period. This thesis presents a comparison of volatility models incorporating economic intuition, sentiment, historical values of volatility and stochastics. By exploiting intra-day at 5 min interval the trade-off between noise and loss of valuable information effectively kept at a minimum yielding considerable robustness to the thesis’ result. Linear ARCH-models, Implied Volatility and HARRV applied with the addition of several different combinations of hold-out periods enable multiple vantagepoints for evaluation. This thesis finds HARRV’s series of one-step ahead prediction of future conditional volatility to be superior throughout all hold-out periods. I am able to present empirical evidence supporting the idea that HARRV’s additive cascades of volatility is superior to sentiment-driven implied volatility and ARCH-models pertaining to Nasdaq100.

Covid19 hit the world’s financial markets by surprise in March 2020 and ensuing volatility marked an end to the prior low-volatility environment. This Black Swan engendered numerous publications establishing how the equity market responded to the exogenous shock. However, there is no applicable comparison to Nasdaq100 regarding how models perform during extreme conditions such as ante, amid and post Covid19. Furthermore, goodness of fit together with forecasting accuracy are further examined in the light of new intra-day data from Oxford Man Institute covering this time-period. This thesis presents a comparison of volatility models incorporating economic intuition, sentiment, historical values of volatility and stochastics. By exploiting intra-day at 5 min interval the trade-off between noise and loss of valuable information effectively kept at a minimum yielding considerable robustness to the thesis’ result. Linear ARCH-models, Implied Volatility and HARRV applied with the addition of several different combinations of hold-out periods enable multiple vantagepoints for evaluation. This thesis finds HARRV’s series of one-step ahead prediction of future conditional volatility to be superior throughout all hold-out periods. I am able to present empirical evidence supporting the idea that HARRV’s additive cascades of volatility is superior to sentiment-driven implied volatility and ARCH-models pertaining to Nasdaq100.

Este documento estudia las reacciones de los mercados financieros de Estados Unidos a nuevas noticias de la prensa desde enero de 2019 hasta el primero de mayo de 2020. Con este fin, construimos medidas del contenido y del sentimiento de las noticias mediante el desarrollo de índices apropiados a partir de los titulares y fragmentos de The New York Times, utilizando técnicas de aprendizaje automático no supervisado. En particular, usamos el modelo Asignación Latente de Dirichlet para inferir el contenido (temas) de los artículos, y Word Embedding (implementado con el modelo Skip-gram) y K-Medias para medir su sentimiento (incertidumbre). De esta forma, elaboramos un conjunto de índices de incertidumbre temáticos diarios. Estos índices se utilizan luego para explicar el comportamiento de los mercados financieros de Estados Unidos mediante la implementación de un conjunto de modelos EGARCH. En conclusión, encontramos que dos de los índices de incertidumbre temáticos (uno relacionado con noticias del COVID-19 y otro con noticias de la guerra comercial) explican gran parte de los movimientos en los mercados financieros desde principios de 2019 hasta los cuatro primeros meses de 2020. Además, encontramos que el índice de incertidumbre temático relacionado con la economía y la Reserva Federal está positivamente relacionado con los mercados financieros, capturando las acciones de la Reserva Federal durante períodos de incertidumbre., This paper investigates the reactions of US financial markets to press news from January 2019 to 1 May 2020. To this end, we deduce the content and sentiment of the news by developing apposite indices from the headlines and snippets of The New York Times, using unsupervised machine learning techniques. In particular, we use Latent Dirichlet Allocation to infer the content (topics) of the articles, and Word Embedding (implemented with the Skip-gram model) and K-Means to measure their sentiment (uncertainty). In this way, we arrive at the definition of a set of daily topic-specific uncertainty indices. These indices are then used to find explanations for the behaviour of the US financial markets by implementing a batch of EGARCH models. In substance, we find that two topic-specific uncertainty indices, one related to COVID-19 news and the other to trade war news, explain the bulk of the movements in the financial markets from the beginning of 2019 to end-April 2020. Moreover, we find that the topic-specific uncertainty index related to the economy and the Federal Reserve is positively related to the financial markets, meaning that our index is able to capture actions of the Federal Reserve during periods of uncertainty.

This study empirically examined the asymmetric oil price shocks in Nigeria from 1981q1-2019q4 using the Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model. The EGARCH model was employed to investigate the asymmetric oil price shocks by obtaining the conditional variance from the estimated results. Empirical results revealed a weak indication for leverage effect and a strong indication for asymmetric effect. The positive egarch (L2) coefficient means that unanticipated increases in the price crude Oil are more profitable than unanticipated decreases in the price of crude Oil. Also, the results revealed strong asymmetry of oil price shocks in Nigeria. In specific terms, the positive asymmetric coefficient (1.8276) means an observed tendency of the crude oil price shock to be higher by approximately 1.83 per cent in declining oil prices in the crude oil market than in rising prices in the oil markets. Based on the above, the study recommended appropriate export diversification policies to reduce the dependency on crude oil exports as the major export (revenue) in the economy. This will offset crude oil price shocks such as the COVID-19 pandemic shock on Oil price, especially from an unanticipated decrease in crude oil prices in the international market. Key Words: Oil price, Oil Price Shocks, Asymmetry, EGARCH, Nigeria

Cryptocurrencies are highly volatile and risky assets, therefore, it is of vital importance to find an appropriate model for risk measurement. This thesis compares three parametric and three non-parametric estimation methods to estimate the value at risk and the expected shortfall of five cryptocurrencies, namely Bitcoin (BTC), Ethereum (ETH), Binance coin (BNB), Ripple coin (XRP), and Cardano (ADA). We estimate the value at risk and expected shortfall using these methods at the confidence level of 95% and 99%. We then perform five backtesting procedures and use these test results to compare the performance of these estimation methods. Consequently, we can conclude that the volatility-weighted historical simulation (VWHS) method using the exponential weighted moving average (EWMA) model and GARCH-type models to rescale cryptocurrency loss for VaR and ES estimation perform the best in most cases. The basic historical simulation (BHS) method and the peak over threshold (POT) method also show positive performance in several cases. Meanwhile, the age-weighted historical simulation (AWHS) has a poor performance in almost all cases.

This study empirically examined the asymmetric oil price shocks in Nigeria from 1981q1-2019q4 using the Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model. The EGARCH model was employed to investigate the asymmetric oil price shocks by obtaining the conditional variance from the estimated results. Empirical results revealed a weak indication for leverage effect and a strong indication for asymmetric effect. The positive egarch (L2) coefficient means that unanticipated increases in the price crude Oil are more profitable than unanticipated decreases in the price of crude Oil. Also, the results revealed strong asymmetry of oil price shocks in Nigeria. In specific terms, the positive asymmetric coefficient (1.8276) means an observed tendency of the crude oil price shock to be higher by approximately 1.83 per cent in declining oil prices in the crude oil market than in rising prices in the oil markets. Based on the above, the study recommended appropriate export diversification policies to reduce the dependency on crude oil exports as the major export (revenue) in the economy. This will offset crude oil price shocks such as the COVID-19 pandemic shock on Oil price, especially from an unanticipated decrease in crude oil prices in the international market. Key Words: Oil price, Oil Price Shocks, Asymmetry, EGARCH, Nigeria

How do financial markets react to populist electoral success? Theoretically, the effect can go in one of two directions. In the first instance, populists tend to espouse resolutely anti-finance ideas, and thus a populist wave would be expected to be bad for financial returns across the board. On the other hand, populists also tend to enact various stimulus and redistributive schemes, and these policies could also give a boost to financial markets. Additionally, in the long-term, if populists become entrenched, they take over the commanding heights, meaning a need for functioning financial markets in order to provide capital for the elites. Utilizing new advances in the measurement of populism, this paper amasses a database of populist advances across developed economies since 2008 and arrays them against equity market performance. Using EGARCH-M volatility modelling on pooled data and event studies on specific episodes of populist success, this analysis reveals that a) populism's effect in the short run is mainly through volatility channels and b) populism's longer-term effects are highly dependent on the specific brand of populism and the country context in which populism operates.

Purpose: The research aims to build a suitable model for the conditional mean and conditional variance for forecasting the rate of inflation in Pakistan by summarizing the properties of the series and characterizing its salient features. Design/Methodology/Approach: For this purpose, Pakistan’s Inflation Rate is based upon the Consumer Price Index (CPI), ranging from January 1962 to December 2019 has been analyzed. Augmented Dickey Fuller (ADF) test that was used for testing the stationarity of the series. The ARIMA modeling technique is a conditional mean and GARCH model for conditional variance. Models are selected on AIC and BIC model selection criteria. The estimating and forecasting ability of three ARIMA models with the GARCH (2,2) model has been compared to capture the possible nonlinearity present in the data. To depict the possible asymmetric effect in the conditional variance, two asymmetric GARCH models, EGARCH and TGARCH models have been applied. Findings: Based on statistical loss functions, GARCH (2,2) model is the best variance model for this series. The empirical results reveal that the performance of model-2 is best for all the three variance models. However, the GARCH model is the best as the variance model for this series. This shows that the asymmetric effect invariance is not so important for the rate of inflation in Pakistan.  Implications/Originality/Value: The current study was based on the least considered variables and the pioneer in testing the complex relationship through the ARIMA model with GARCH innovation.

We analyze the impact of the COVID-19 pandemic on the conditional variance of stock returns. We look at this effect from a global perspective, so we employ series of major stock market and sector indices. We use the Hansen’s Skewed-t distribution with EGARCH extended to control for sudden changes in volatility. We oversee the COVID-19 effect on measures of downside risk such as the Value-at-Risk. Our results show that there is a significant sudden shift up in the return distribution variance post the announcement of the pandemic, which must be explained properly to obtain reliable measures for financial risk management.

Purpose: The research aims to build a suitable model for the conditional mean and conditional variance for forecasting the rate of inflation in Pakistan by summarizing the properties of the series and characterizing its salient features. Design/Methodology/Approach: For this purpose, Pakistan’s Inflation Rate is based upon the Consumer Price Index (CPI), ranging from January 1962 to December 2019 has been analyzed. Augmented Dickey Fuller (ADF) test that was used for testing the stationarity of the series. The ARIMA modeling technique is a conditional mean and GARCH model for conditional variance. Models are selected on AIC and BIC model selection criteria. The estimating and forecasting ability of three ARIMA models with the GARCH (2,2) model has been compared to capture the possible nonlinearity present in the data. To depict the possible asymmetric effect in the conditional variance, two asymmetric GARCH models, EGARCH and TGARCH models have been applied. Findings: Based on statistical loss functions, GARCH (2,2) model is the best variance model for this series. The empirical results reveal that the performance of model-2 is best for all the three variance models. However, the GARCH model is the best as the variance model for this series. This shows that the asymmetric effect invariance is not so important for the rate of inflation in Pakistan.  Implications/Originality/Value: The current study was based on the least considered variables and the pioneer in testing the complex relationship through the ARIMA model with GARCH innovation.

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.

In recent time the Central Banks cross the globe employ a range of avenues to communicate their monetary policy decisions and explain to financial markets and the general public the reason for their policy actions. This communication, in turn, gives signals to the financial markets regarding the future trajectories of governmental activities. This study therefore investigated the sensitivity of interest rate to MPC communication from 1st January, 2010 to 30th June, 2020 in Nigera. Series of test were carryout and EGARCH was chosen as the appropriate techniques in which dummy variable was used to capture the meeting days in the variance equation. Data of monetary policy were sourced from CBN website. The results of an EGARCH model show that the communications between Central Bank and the money market are considerably informative and therefore assist to reduce market interest rates' volatility. The study has so concluded that the communication from the Central Bank of Nigeria has an impact on the desired direction of interests. One policy implication of this conclusion is that it is clear enough about the desired policy orientation for the future that CBN communique substance of MPC meetings will guide the market in the proper way. This is consistent with the literature that if Central Bank opens the foundations for monetary policy implementation up to the markets, it raises the odds of controlling agents' expectations. Therefore the study recommends that the meeting should be sustained.

In recent time the Central Banks cross the globe employ a range of avenues to communicate their monetary policy decisions and explain to financial markets and the general public the reason for their policy actions. This communication, in turn, gives signals to the financial markets regarding the future trajectories of governmental activities. This study therefore investigated the sensitivity of interest rate to MPC communication from 1st January, 2010 to 30th June, 2020 in Nigera. Series of test were carryout and EGARCH was chosen as the appropriate techniques in which dummy variable was used to capture the meeting days in the variance equation. Data of monetary policy were sourced from CBN website. The results of an EGARCH model show that the communications between Central Bank and the money market are considerably informative and therefore assist to reduce market interest rates' volatility. The study has so concluded that the communication from the Central Bank of Nigeria has an impact on the desired direction of interests. One policy implication of this conclusion is that it is clear enough about the desired policy orientation for the future that CBN communique substance of MPC meetings will guide the market in the proper way. This is consistent with the literature that if Central Bank opens the foundations for monetary policy implementation up to the markets, it raises the odds of controlling agents' expectations. Therefore the study recommends that the meeting should be sustained.

Purpose: The research aims to build a suitable model for the conditional mean and conditional variance for forecasting the rate of inflation in Pakistan by summarizing the properties of the series and characterizing its salient features. Design/Methodology/Approach: For this purpose, Pakistan’s Inflation Rate is based upon the Consumer Price Index (CPI), ranging from January 1962 to December 2019 has been analyzed. Augmented Dickey Fuller (ADF) test that was used for testing the stationarity of the series. The ARIMA modeling technique is a conditional mean and GARCH model for conditional variance. Models are selected on AIC and BIC model selection criteria. The estimating and forecasting ability of three ARIMA models with the GARCH (2,2) model has been compared to capture the possible nonlinearity present in the data. To depict the possible asymmetric effect in the conditional variance, two asymmetric GARCH models, EGARCH and TGARCH models have been applied. Findings: Based on statistical loss functions, GARCH (2,2) model is the best variance model for this series. The empirical results reveal that the performance of model-2 is best for all the three variance models. However, the GARCH model is the best as the variance model for this series. This shows that the asymmetric effect invariance is not so important for the rate of inflation in Pakistan.  Implications/Originality/Value: The current study was based on the least considered variables and the pioneer in testing the complex relationship through the ARIMA model with GARCH innovation.

Purpose: The research aims to build a suitable model for the conditional mean and conditional variance for forecasting the rate of inflation in Pakistan by summarizing the properties of the series and characterizing its salient features. Design/Methodology/Approach: For this purpose, Pakistan’s Inflation Rate is based upon the Consumer Price Index (CPI), ranging from January 1962 to December 2019 has been analyzed. Augmented Dickey Fuller (ADF) test that was used for testing the stationarity of the series. The ARIMA modeling technique is a conditional mean and GARCH model for conditional variance. Models are selected on AIC and BIC model selection criteria. The estimating and forecasting ability of three ARIMA models with the GARCH (2,2) model has been compared to capture the possible nonlinearity present in the data. To depict the possible asymmetric effect in the conditional variance, two asymmetric GARCH models, EGARCH and TGARCH models have been applied. Findings: Based on statistical loss functions, GARCH (2,2) model is the best variance model for this series. The empirical results reveal that the performance of model-2 is best for all the three variance models. However, the GARCH model is the best as the variance model for this series. This shows that the asymmetric effect invariance is not so important for the rate of inflation in Pakistan.  Implications/Originality/Value: The current study was based on the least considered variables and the pioneer in testing the complex relationship through the ARIMA model with GARCH innovation.

We analyze the impact of the COVID-19 pandemic on the conditional variance of stock returns. We look at this effect from a global perspective, so we employ series of major stock market and sector indices. We use the Hansen’s Skewed-t distribution with EGARCH extended to control for sudden changes in volatility. We oversee the COVID-19 effect on measures of downside risk such as the Value-at-Risk. Our results show that there is a significant sudden shift up in the return distribution variance post the announcement of the pandemic, which must be explained properly to obtain reliable measures for financial risk management.

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.

Purpose: The research aims to build a suitable model for the conditional mean and conditional variance for forecasting the rate of inflation in Pakistan by summarizing the properties of the series and characterizing its salient features. Design/Methodology/Approach: For this purpose, Pakistan’s Inflation Rate is based upon the Consumer Price Index (CPI), ranging from January 1962 to December 2019 has been analyzed. Augmented Dickey Fuller (ADF) test that was used for testing the stationarity of the series. The ARIMA modeling technique is a conditional mean and GARCH model for conditional variance. Models are selected on AIC and BIC model selection criteria. The estimating and forecasting ability of three ARIMA models with the GARCH (2,2) model has been compared to capture the possible nonlinearity present in the data. To depict the possible asymmetric effect in the conditional variance, two asymmetric GARCH models, EGARCH and TGARCH models have been applied. Findings: Based on statistical loss functions, GARCH (2,2) model is the best variance model for this series. The empirical results reveal that the performance of model-2 is best for all the three variance models. However, the GARCH model is the best as the variance model for this series. This shows that the asymmetric effect invariance is not so important for the rate of inflation in Pakistan.  Implications/Originality/Value: The current study was based on the least considered variables and the pioneer in testing the complex relationship through the ARIMA model with GARCH innovation.

One of the biggest challenges in quantifying joint risk and forming effective policies in financial management and investment strategies is to fully understand the characteristics of market associations in low and high volatility periods. Market interdependence, therefore, is a hot topic that has received interest from academics and industry experts, especially since the Asian Financial Crisis in 1997. China, being the world’s second-largest economy, has been the centre of many studies investigating stock market dependencies. While China has three major share types, namely A-, B- and H-shares, with different market players, market characteristics and operating efficiency, the number of studies on each of these share types remains conservative in comparison to the vast literature on the financial modelling of market interdependencies. Given the need for a more comprehensive understanding of the influence between these share types and other global markets, especially during market turbulences, this thesis examines the cross-market linkages between A-, B- and H-shares in China and several major emerging and advanced markets from 2002 to 2017, which is divided into two non-crisis periods and two crisis periods. This thesis assesses market integration among 17 markets, including asymmetries and leverage effect in the marginal distributions, volatility spillover and tail dependence. The thesis aims to: 1) investigate the univariate asymmetries and leverage effect in the distributional volatility of each time series and to detect volatility spillover between China and other studied markets; 2) assess the dynamic multivariate dependence between China and other studied markets; 3) evaluate the bivariate dependence structure for each of China’s markets and other studied markets using seven different copula functions; and 4) study the multivariate joint tail dependence structure of all studied markets using vine copulas. There are various findings from the thesis. Many advance

One of the implications of the intertemporal capital asset pricing model (CAPM) is that the risk premium of the market portfolio is a linear function of its variance. Yet, estimation theory of classical GARCH-in-mean models with linear-in-variance risk premium requires strong assumptions and is complete. We show that exponential-type GARCH models such as EGARCH or Log-GARCH are more natural in dealing with linear-in-variance risk premia. For the popular and more difficult case of EGARCH-in-mean, we derive conditions for the existence of a unique stationary and ergodic solution and invertibility following a stochastic recurrence equation approach. We then show consistency and asymptotic normality of the quasi maximum likelihood estimator under weak moment assumptions. An empirical application estimates the dynamic risk premia of a variety of stock indices using both EGARCH-M and Log-GARCH-M models.

In the financial industry, it has been increasingly popular to measure risk. One of the most common quantitative measures for assessing risk is Value-at-Risk (VaR). VaR helps to measure extreme risks that an investor is exposed to. In addition to acquiring information of the expected loss, VaR was introduced in the regulatory frameworks of Basel I and II as a standardized measure of market risk. Due to necessity of measuring VaR accurately, this thesis aims to be a contribution to the research field of applying GARCH-models to financial time series in order to forecast the conditional variance and find accurate VaR-estimations. The findings in this thesis is that GARCH-models which incorporate the asymmetric effect of positive and negative returns perform better than a standard GARCH. Further on, leptokurtic distributions have been found to outperform normal distribution. In addition to various models and distributions, various rolling windows have been used to examine how the forecasts differ given window lengths.

This essay investigates how realized variance affects the GARCH-models (GARCH, EGARCH, GJRGARCH) when added as an external regressor. The GARCH models are estimated with three different distributions; Normal-, Student’s t- and Normal inverse gaussian distribution. The results are ambiguous - the models with realized variance improves the model fit, but when applied to forecasting, the models with realized variance are performing similar Value at Risk predictions compared to the models without realized variance.

This study aims to investigate and model statistical properties of Bitcoin and other major cryptocurrencies. There were recent drastic changes in the level of Bitcoin prices as it moved from $740 in 2014 to $19,187 in 2017, and down to $3,830 in 2018. The current study aims to fill the gap in the analysis of cryptoccurencies, primarily Bitcoin returns statistical process. Specifically, the study selects and estimates a model that traces dynamics of returns using ARMA, and also volatility of the residual from the model. To my knowledge, there is gap in the academic literature for the case of Bitcoin to use such approach. The analysis involves data on past daily prices of Bitcoin, in British Pounds and USD, as well as those of Ethereum and Litecoin, both in Pounds. The results obtained from the study provide evidence that ARMA model in combination with eGARCH volatility model can be used for analysis of statistical process of Bitcoin returns. Moreover, significant statistical differences are identified between Bitcoin prices in UK Pounds and US Dollars. Although there is no evidence that shows the price level has an effect on volatility, significant decline is identified in the volatility of Bitcoin log-returns since 2018 as compared to the previous period. For each considered cryptocurrency, the current study determines the optimal specification of ARMA model, as well as GARCH-type model and optimal statistical distribution of the residual. The set of results can be used to estimate statistical process behind the cryptocurrency historical prices. Moreover, relation between ARMA(p, q) lag order, and type of optimal volatility model and residual distribution is explored, no significant relation is identified.

The volatility spillover is defined as the transmission of instability from market to market. It occurs when the volatility price change in one market causes a lagged impact on volatility price in another market above the local effects of market. In this study the garchmodels are used to examine the possibility of volatility transmission between the KSE100 index (Pakistan) and S&P500 index (usa); in other words, to examine how the volatility in one market mayinfluence the other and vice versa. The egarchmodel is also applied and it was observed thatour attempt to analyze symmetry and persistence in the KSE100 index and the S&P500 index volatility proved that there is clear evidence that shocks to the volatitlity of the KSE100 and S&P500 indexes have asymmetric and persistent effects. It is observed from the study that the shocks to the stock returns in one market do not transmit to the other; in other words, it appears that there is no spillover effect between the two stock markets., O derramamento volátil é definido como a instabilidade entre mercados. Acontece quando o preço da volatilidade muda em um mercado causando um impacto atrasado no preço da volatilidade em outro mercado que se encontra por cima dos efeitos locais do mercado. Neste estudo os modelos GARCH são utilizados paraexaminar a possibilidade de transmissão de volatilida de entre o índice KSE100 (Paquistão) e o índice S&P500 (Estados Unidos). Em outras palavras, para examinar a influência da volatilidade em outro e vice-versa. O modelo EGCARCH também foi aplicado e se observa nossa tentativa por analisar a simetria e a persistência da volatilidade no KSE100 e o S&P500, se evidencia com claridade que choques na volatilidade de ambos os dois tem um efeito assimétrico e persistente. A partir do estudo se observou que os choques ao rendimento das ações em um mercado não se transmitem ao outro, em outras palavras, não há presença de efeito de derramamento entre as duas bolsas de Valores., El derrame volátil es definido como la inestabilidad entre mercados. Sucede cuando el precio de la volatilidad cambia en un mercado causando un impacto rezagado en el precio de la volatilidad en otro mercado que se encuentra por encima los efectos locales del mercado. En este estudio los modelos GARCH son utilizados para examinar la posiblidad de transmición de volatilidad entre el índice KSE100( Pakistan) y el índice S&P500 (Estados Unidos). En otras palabras, para examinar la influencia de la volatilidad en otro y vice versa. El modelo EGCARCH también fue aplicado y se observa nuestro intento por analizar la simetría y la persistencia de lavolatilidad en el KSE100 y el S&P500, se evidencia con claridad que choques en la volatilidad de ambos tiene un efecto asimetrico y persistente. A partir del estudio se observó que los choques al rendimiento de las acciones en un mercado no se transmiten al otro, en otras palabras, no hay presencia de efecto de derrame entre las dos bolsas de Valores.

The volatility spillover is defined as the transmission of instability from market to market. It occurs when the volatility price change in one market causes a lagged impact on volatility price in another market above the local effects of market. In this study the garchmodels are used to examine the possibility of volatility transmission between the KSE100 index (Pakistan) and S&P500 index (usa); in other words, to examine how the volatility in one market mayinfluence the other and vice versa. The egarchmodel is also applied and it was observed thatour attempt to analyze symmetry and persistence in the KSE100 index and the S&P500 index volatility proved that there is clear evidence that shocks to the volatitlity of the KSE100 and S&P500 indexes have asymmetric and persistent effects. It is observed from the study that the shocks to the stock returns in one market do not transmit to the other; in other words, it appears that there is no spillover effect between the two stock markets., O derramamento volátil é definido como a instabilidade entre mercados. Acontece quando o preço da volatilidade muda em um mercado causando um impacto atrasado no preço da volatilidade em outro mercado que se encontra por cima dos efeitos locais do mercado. Neste estudo os modelos GARCH são utilizados paraexaminar a possibilidade de transmissão de volatilida de entre o índice KSE100 (Paquistão) e o índice S&P500 (Estados Unidos). Em outras palavras, para examinar a influência da volatilidade em outro e vice-versa. O modelo EGCARCH também foi aplicado e se observa nossa tentativa por analisar a simetria e a persistência da volatilidade no KSE100 e o S&P500, se evidencia com claridade que choques na volatilidade de ambos os dois tem um efeito assimétrico e persistente. A partir do estudo se observou que os choques ao rendimento das ações em um mercado não se transmitem ao outro, em outras palavras, não há presença de efeito de derramamento entre as duas bolsas de Valores., El derrame volátil es definido como la inestabilidad entre mercados. Sucede cuando el precio de la volatilidad cambia en un mercado causando un impacto rezagado en el precio de la volatilidad en otro mercado que se encuentra por encima los efectos locales del mercado. En este estudio los modelos GARCH son utilizados para examinar la posiblidad de transmición de volatilidad entre el índice KSE100( Pakistan) y el índice S&P500 (Estados Unidos). En otras palabras, para examinar la influencia de la volatilidad en otro y vice versa. El modelo EGCARCH también fue aplicado y se observa nuestro intento por analizar la simetría y la persistencia de lavolatilidad en el KSE100 y el S&P500, se evidencia con claridad que choques en la volatilidad de ambos tiene un efecto asimetrico y persistente. A partir del estudio se observó que los choques al rendimiento de las acciones en un mercado no se transmiten al otro, en otras palabras, no hay presencia de efecto de derrame entre las dos bolsas de Valores.

This study aims to investigate and model statistical properties of Bitcoin and other major cryptocurrencies. There were recent drastic changes in the level of Bitcoin prices as it moved from $740 in 2014 to $19,187 in 2017, and down to $3,830 in 2018. The current study aims to fill the gap in the analysis of cryptoccurencies, primarily Bitcoin returns statistical process. Specifically, the study selects and estimates a model that traces dynamics of returns using ARMA, and also volatility of the residual from the model. To my knowledge, there is gap in the academic literature for the case of Bitcoin to use such approach. The analysis involves data on past daily prices of Bitcoin, in British Pounds and USD, as well as those of Ethereum and Litecoin, both in Pounds. The results obtained from the study provide evidence that ARMA model in combination with eGARCH volatility model can be used for analysis of statistical process of Bitcoin returns. Moreover, significant statistical differences are identified between Bitcoin prices in UK Pounds and US Dollars. Although there is no evidence that shows the price level has an effect on volatility, significant decline is identified in the volatility of Bitcoin log-returns since 2018 as compared to the previous period. For each considered cryptocurrency, the current study determines the optimal specification of ARMA model, as well as GARCH-type model and optimal statistical distribution of the residual. The set of results can be used to estimate statistical process behind the cryptocurrency historical prices. Moreover, relation between ARMA(p, q) lag order, and type of optimal volatility model and residual distribution is explored, no significant relation is identified.

This essay investigates how realized variance affects the GARCH-models (GARCH, EGARCH, GJRGARCH) when added as an external regressor. The GARCH models are estimated with three different distributions; Normal-, Student’s t- and Normal inverse gaussian distribution. The results are ambiguous - the models with realized variance improves the model fit, but when applied to forecasting, the models with realized variance are performing similar Value at Risk predictions compared to the models without realized variance.

In the financial industry, it has been increasingly popular to measure risk. One of the most common quantitative measures for assessing risk is Value-at-Risk (VaR). VaR helps to measure extreme risks that an investor is exposed to. In addition to acquiring information of the expected loss, VaR was introduced in the regulatory frameworks of Basel I and II as a standardized measure of market risk. Due to necessity of measuring VaR accurately, this thesis aims to be a contribution to the research field of applying GARCH-models to financial time series in order to forecast the conditional variance and find accurate VaR-estimations. The findings in this thesis is that GARCH-models which incorporate the asymmetric effect of positive and negative returns perform better than a standard GARCH. Further on, leptokurtic distributions have been found to outperform normal distribution. In addition to various models and distributions, various rolling windows have been used to examine how the forecasts differ given window lengths.

The number of Chinese tourists visiting Taiwan has been closely related to the political relationship across the Taiwan Strait. The occurrence of political events and disasters or accidents have had, and will continue to have, a huge impact on the Taiwan tourism market. To date, there has been relatively little empirical research conducted on this issue. Tourists are characterized as being involved in one of three types of tourism: group tourism (group-type), individual tourism (individual-type), and medical cosmetology (medical-type). We use the fundamental equation in tourism finance to examine the correlation that exists between the rate of change in the number of tourists and the rate of return on tourism. Second, we use the event study method to observe whether the numbers of tourists have changed abnormally before and after the occurrence of major events on both sides of the Strait. Three different types of conditional variance models, namely, the Generalized Autoregressive Conditional Heteroscedasticity, GARCH (1,1), Glosten, Jagannathan and Runkle, GJR (1,1) and Exponential GARCH, EGARCH (1,1), are used to estimate the abnormal rate of change in the number of tourists. The empirical results concerning the major events affecting the changes in the numbers of tourists from China to Taiwan are economically significant, and confirm the types of tourists that are most likely to be affected by such major events.

In today’s financial markets, volatility is a fundamental concept in regards of the risk assessment of assets and instruments. Financial volatility is commonly used to measure the quantitative aspects of risk and is given a significant amount of attention in past literature and research. The leverage effect refers to the well-established negative relationship between return and future volatility. The relation is usually explained by the increased leverage ratio that arises from a drop in the share price for a firm. A lower price means lower value of the equity and while the debt remains unchanged, the leverage ratio will rise. The leverage ratio affect how risky the equity is from an investor’s perspective, hence affects the volatility of the stock. This paper aims to analyse whether the theory is applicable on the Swedish stock exchange and takes both individual stocks and the OMXS30-index into account. Further theories related to the model is acknowledged in order to enhance the analysis of the findings. The study is performed by a regression model where volatility, estimated through an EGARCH model, represents the dependent variable. Lagged return, together with a number of control variables, constitutes the explanatory variables. The findings claims that the leverage effect is present for individual stocks but can be rejected on the index level. Additionally, significant improvement was noticed when a dynamic approach was added to the model. The conclusions drawn is that the Swedish stock exchange facilitates the leverage effect for individual firms but it is off-set by other theories such as risk-return trade-off and volatility clustering for the index., I dagens finansiella marknader är volatilitet ett fundamentalt koncept som är ytterst relevant i risk bedömningen av tillgångar och instrument. Finansiell volatilitet används ofta för att mäta risk i kvantitativ form och har på senare tiden uppmärksammats i allt större utsträckning. Leverage effekten (en.”the leverage effect”) refererar till det! väletablerade negativa samband som finns mellan avkastning i nuvarande period och framtida volatilitet. Sambandet mellan dessa faktorer har av många förklarats av en ökning i skuldsättningsgraden för ett företag. Skuldsättningsgraden ökar enligt teorin som en konsekvens av att aktiekursen sjunker, innebärande en värdeminskning av det egna kapitalet, samtidigt som skulderna förblir oförändrade. Skuldsättningsgraden påverkar i sin tur aktiens volatilitet genom en uppfattning av hur stor risk som kan förknippas med en investering i aktien. För att stärka analysen diskuteras, förutom leverage effekten, ett antal teorier som kan relateras till modellen. Uppsatsen syfte är att avgöra om leverage effekten är signifikant applicerbar på den svenska aktiemarknaden, både för individuella aktier samt OMXS30 indexet. Studien utförs genom en regressions modell där volatiliteten, estimerad genom en EGARCH model, representerar den beroende variabeln. Avkastningen i föregående period samt ett antal kontroll variabler utgör de oberoende variablerna. Resultatet visar att leverage effekten har stor applicerbarhet på de individuella aktierna men kan uteslutas på en index nivå. Dessutom ökar relevansen signifikant när en dynamisk angreppsätt adderades till modellen. Slutsatsen är att leverage effekten är närvarande på en individuell nivå men neutraliseras av teorier så som ”risk return trade off” och ”volatilitets klustring” på index nivå.

The objective of this paper is to replicate the results in Kristoufek (2014) on the leverage effect in energy futures and to analyze its robustness to both the methodology and the type of returns used. We first apply correlation-based tools for detecting both conditional heteroscedasticity and leverage effect. Then, we estimate asymmetric and long memory GARCH-type models using the data provided by Kristoufek (2014) by considering different software and the possibility that innovations follow a non-Gaussian distribution. Our findings confirm most of the results in the replicated paper. In particular, we can strongly confirm there is a significant leverage effect in the return series of WTI (West Texas Intermediate) and Brent crude oils. For the heating oil and the natural gas series, the statistical significance of the leverage effect depends on both the methodology and the type of returns used.

By betting on market downturns, short sellers make profits from asset declines. Thus, critics often blame short sellers for being responsible for market downturns and as a consequence, short selling restrictions became a popular phenomenon worldwide post the 2008 financial crisis. During the European sovereign debt crisis regulators in France, Belgium, Spain and Italy imposed a short selling bans for financial stocks in order to prevent further market downturns. The ban, with the purpose of reducing market volatility and the effect of false rumours, was active between August 2011 and February 2012. This paper studies the impact on market volatility from this short selling ban and attempts to ascertain whether or not it achieved its objective. In order to test for the stock market volatility in the four European countries where the ban was imposed, we use a variety of Generalised Autoregressive Conditional Heteroskedasticity (GARCH) models. We apply these models to portfolios of stocks that were subject to a short selling ban, as well as to portfolios of stocks that were not. We find some evidence of an increase in the volatility of returns for stocks on which short selling was not banned and attempt to explain why this is the case.

The objective of this paper is to replicate the results in Kristoufek (2014) on the leverage effect in energy futures and to analyze its robustness to both the methodology and the type of returns used. We first apply correlation-based tools for detecting both conditional heteroscedasticity and leverage effect. Then, we estimate asymmetric and long memory GARCH-type models using the data provided by Kristoufek (2014) by considering different software and the possibility that innovations follow a non-Gaussian distribution. Our findings confirm most of the results in the replicated paper. In particular, we can strongly confirm there is a significant leverage effect in the return series of WTI (West Texas Intermediate) and Brent crude oils. For the heating oil and the natural gas series, the statistical significance of the leverage effect depends on both the methodology and the type of returns used.

By betting on market downturns, short sellers make profits from asset declines. Thus, critics often blame short sellers for being responsible for market downturns and as a consequence, short selling restrictions became a popular phenomenon worldwide post the 2008 financial crisis. During the European sovereign debt crisis regulators in France, Belgium, Spain and Italy imposed a short selling bans for financial stocks in order to prevent further market downturns. The ban, with the purpose of reducing market volatility and the effect of false rumours, was active between August 2011 and February 2012. This paper studies the impact on market volatility from this short selling ban and attempts to ascertain whether or not it achieved its objective. In order to test for the stock market volatility in the four European countries where the ban was imposed, we use a variety of Generalised Autoregressive Conditional Heteroskedasticity (GARCH) models. We apply these models to portfolios of stocks that were subject to a short selling ban, as well as to portfolios of stocks that were not. We find some evidence of an increase in the volatility of returns for stocks on which short selling was not banned and attempt to explain why this is the case.

In today’s financial markets, volatility is a fundamental concept in regards of the risk assessment of assets and instruments. Financial volatility is commonly used to measure the quantitative aspects of risk and is given a significant amount of attention in past literature and research. The leverage effect refers to the well-established negative relationship between return and future volatility. The relation is usually explained by the increased leverage ratio that arises from a drop in the share price for a firm. A lower price means lower value of the equity and while the debt remains unchanged, the leverage ratio will rise. The leverage ratio affect how risky the equity is from an investor’s perspective, hence affects the volatility of the stock. This paper aims to analyse whether the theory is applicable on the Swedish stock exchange and takes both individual stocks and the OMXS30-index into account. Further theories related to the model is acknowledged in order to enhance the analysis of the findings. The study is performed by a regression model where volatility, estimated through an EGARCH model, represents the dependent variable. Lagged return, together with a number of control variables, constitutes the explanatory variables. The findings claims that the leverage effect is present for individual stocks but can be rejected on the index level. Additionally, significant improvement was noticed when a dynamic approach was added to the model. The conclusions drawn is that the Swedish stock exchange facilitates the leverage effect for individual firms but it is off-set by other theories such as risk-return trade-off and volatility clustering for the index., I dagens finansiella marknader är volatilitet ett fundamentalt koncept som är ytterst relevant i risk bedömningen av tillgångar och instrument. Finansiell volatilitet används ofta för att mäta risk i kvantitativ form och har på senare tiden uppmärksammats i allt större utsträckning. Leverage effekten (en.”the leverage effect”) refererar till det! väletablerade negativa samband som finns mellan avkastning i nuvarande period och framtida volatilitet. Sambandet mellan dessa faktorer har av många förklarats av en ökning i skuldsättningsgraden för ett företag. Skuldsättningsgraden ökar enligt teorin som en konsekvens av att aktiekursen sjunker, innebärande en värdeminskning av det egna kapitalet, samtidigt som skulderna förblir oförändrade. Skuldsättningsgraden påverkar i sin tur aktiens volatilitet genom en uppfattning av hur stor risk som kan förknippas med en investering i aktien. För att stärka analysen diskuteras, förutom leverage effekten, ett antal teorier som kan relateras till modellen. Uppsatsen syfte är att avgöra om leverage effekten är signifikant applicerbar på den svenska aktiemarknaden, både för individuella aktier samt OMXS30 indexet. Studien utförs genom en regressions modell där volatiliteten, estimerad genom en EGARCH model, representerar den beroende variabeln. Avkastningen i föregående period samt ett antal kontroll variabler utgör de oberoende variablerna. Resultatet visar att leverage effekten har stor applicerbarhet på de individuella aktierna men kan uteslutas på en index nivå. Dessutom ökar relevansen signifikant när en dynamisk angreppsätt adderades till modellen. Slutsatsen är att leverage effekten är närvarande på en individuell nivå men neutraliseras av teorier så som ”risk return trade off” och ”volatilitets klustring” på index nivå.

For many developing countries, historical inflation figures are rarely available. We propose a simple method that aims to recover such figures of inflation using prices of postage stamps issued in earlier years. We illustrate our method for Suriname, where annual inflation rates are available for 1961 until 2015, and where fluctuations in inflation rates are prominent. We estimate the inflation rates for the sample 1873 to 1960. Our main finding is that high inflation periods usually last no longer than 2 or 3 years. An Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH) model for the recent sample and for the full sample with the recovered inflation rates shows the relevance of adding the recovered data

In the class of univariate conditional volatility models, the three most popular are the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten et al. (1992), and the exponential GARCH (or EGARCH) model of Nelson (1990, 1991). For purposes of deriving the mathematical regularity properties, including invertibility that relates the standardized residuals to the returns shocks, to determine the likelihood function for estimation, and the statistical conditions to establish asymptotic properties, it is essential to understand the stochastic properties underlying the three univariate models. The random coefficient autoregressive process was used to obtain GARCH by Tsay (1987), an extension of which was used by McAleer (2014) to obtain GJR. A random coefficient complex nonlinear moving average process was used by McAleer and Hafner (2014) to obtain EGARCH. These models can be used to capture asymmetry, which denotes the different impacts on conditional volatility of positive and negative shocks of equal magnitude, and possibly also leverage, which is the negative correlation between returns shocks and subsequent shocks to volatility (see Black 1976). McAleer (2014) showed that asymmetry was possible for GJR, but not leverage. McAleer and Hafner (2014) showed that leverage was not possible for EGARCH. Surprisingly, the condition for asymmetry in EGARCH seem to have been ignored in the literature, or has concentrated on the incorrect parametric condition, with no clear explanation, and hence with associated unclear and misleading interpretations. The purpose of the paper is to derive the regularity condition for asymmetry in EGARCH, and to provide the correct interpretation. It is shown that, in practice, EGARCH always displays asymmetry, though not leverage.

Inledning: Företagsförvärv har länge varit en metod som företag tillämpar i syfte att skapa tillväxt. Samtidigt har investerare som mål att skapa sig en så stor avkastning på investerat kapital som möjligt vilket innebär att det gäller att vara snabb med att identifiera vilka företag som har potentialen att öka i värde. När ett rykte om ett företagsförvärv når investerare kan det leda till att ett intresse väcks samt lockar till investering i något av de aktuella företagen. Detta kan i sin tur generera hög avkastning för investerare utan att ryktet har bekräftats. Syfte: Syftet med studien är att undersöka huruvida rykten om företagsförvärv påverkar aktiemarknadens syn på dess värdering. Vidare syftar denna studie till att undersöka om det föreligger några skillnader på ryktets påverkan mellan olika marknader. Metod: Studien angriper ämnet genom ett kvantitativt förhållningssätt. Studien behandlar insamlade sekundärdata via databasen ORBIS samt Google Finance. MacKinlays modell för eventstudier har implementerats för att mäta den abnormala avkastningen och en regressionsanalys tillämpats med hjälp av modellerna EGARCH samt Ordinary Least Squares (OLS). Slutsats: Amerikanska och brittiska marknaden påvisar abnormal avkastning i koppling till rykten om företagsförvärv. Den abnormala avkastningen skiljer sig mellan marknaderna vilket visar på en skillnad i reaktionen på respektive marknad där amerikanska marknaden uppmäter en negativ abnormal avkastning till skillnad från brittiska marknaden där en positiv abnormal avkastning uppmätts., Introduction: Acquisitions has been a tool with the goal of creating growth for companies for a long time. At the same time, investors always strive to allocate their investments to receive as good of a return for their invested capital as possible. This means that investors must quickly identify the optimal investment that have the potential to grow in value in the stock market. When a rumor of a business acquisition is spread, the effect can be a business opportunity regarding the target company for the markets investors which can lead to investors earning a fortune on the market’s reaction without the conformation of the rumor. Purpose: The purpose of the thesis is to examine whether rumors of acquisitions affect the stock market's evaluation of the target company's value. Further purpose of the thesis is to examine if there is a difference between different markets regarding the rumors affect. Method: The thesis is examined by a quantitative research method with secondary data from the database ORBIS and Google Finance. The research model is a general event study designed by Craig MacKinlay with the implementation of the regression model EGARCH and Ordinary Least Squares (OLS). Conclusion: The American and British market demonstrates an abnormal return connected to the rumor of a business acquisitions. The reaction differs between the markets which indicates a difference in reaction towards rumors of business acquisitions. The American market show an abnormal decrease in the markets value whereas the British market show an abnormal increase in its market value.

The topic of this thesis is the leverage effect i.e. asymmetric volatility. The leverage effect describes the negative relationship between asset value and volatility. The purpose is to examine if firm specific variables impact the size of the leverage effect, in order to bring additional insights into the missing gap in the research field. The study is conducted on 1,311 U.S. companies active on NASDAQ or the New York Stock Exchange (NYSE) between 1996 and 2015. Two GARCH models are applied to estimate the asymmetric volatility; the GJR-GARCH(1,1) and the EGARCH(1,1) models. Panel data models are used in order to investigate how the firm specific variables influence the leverage effect. The findings of this paper show that two out of the eight used variables significantly impact the leverage effect; the firm size and the beta. One of the variables deemed insignificant is the debt-to-equity ratio, which contradicts the original hypothesis behind the leverage effect by Black (1976). Thus, this study concludes that firm specific variables impact the size of the leverage effect. However, the deemed insignificance for six of the variables show that not all variables influence the leverage effect. Furthermore, the sign and the size of the coefficients differ between the variables, with some being more influential than others.

This thesis examines multiple ARCH-family models' volatility forecasting performance on the London Bullion Market Gold price, the OMXS30, and the USD/EUR exchange rate. Further, this thesis uses two different time periods to exploit differences and similarities in the forecast accuracy among the conditional variance models. The models we examine are the ARCH, the GARCH, the IGARCH, the EGARCH, and the GJR-GARCH model. Furthermore, we divide each period into an in-sample and an out-of-sample period. The models are estimated in the in-sample period and then used to forecast the volatility in the out-of-sample period. This thesis uses the squared reutrns as an unbiased approximation of the latent volatility. The forecasts are evaluated using two loss functions, the mean absolute error and the mean squared error. The results indicate a very inconsistent ranking among the models. None of the models seem superior to the other models, based on both loss functions, when forecasting the conditional volatilit in the different assets and periods. However, the ARCH models seems to perform well relative the other models, when forecasting the volatility of the gold using only the mean absolute error as a tool to evaluate the forecasts.

Today’s society requires an endless supply of energy resources to keep functioning properly. The fluctuations in the prices of energy commodities are always a concern as it affects not only investors, but regular households as well. With the general turmoil the market is experiencing, the necessity for risk management has become of outmost importance. Thus, this paper provides an empirical study of the determination of the risk for four different energy commodities. The focus is on crude oil (WTI), gasoline, natural gas and coal, as they represent most of the world’s energy consumption of today. The time periods from 2010 to 2016 will be analyzed as it represents a new period of increased volatility. The empirical research presented consists of calculating Value-at-Risk (VaR) for Value Weighted Historical Simulation (VWHS), Student’s t-distribution and the EVT Conditional Peaks over Threshold (POT) approaches together with three different volatility estimates, Generalized Autoregressive Conditional Heteroskedasticity (GARCH (1.1)), Exponentional GARCH (EGARCH) and Threshold GARCH (TGARCH). The different modeling approaches of volatility estimations will account for price asymmetries in the distributions. Based of the empirical results, the study indicates that the Student’s t-distribution with the EGARCH volatility process is the preferred method for VaR estimation.

The Chinese stock market has been established for more than 20 years. Although it is not as mature as the highly developed western securities markets, it has a huge influence on the global economy. It is significant to study the risks of the Chinese stock market, especially the risk of stock indexes. Affected by the economic globalization today, more and more financial derivatives and financial instruments appear which may lead to the increase of related risk so that the demand of research on the risk of the financial market is also getting higher and higher. Risk measurement is a key in risk management, and its measurement methods are constantly evolving. Value at Risk (VaR) method is one of the effective methods to measure the financial risk, which is widely used in domestic and foreign financial institutions. Compared with traditional models, it has much more accuracy and reasonability and is much easier to implement. As the two main indexes in Chinese stock market, the Shanghai Composite stock index and the Shenzhen Component index are selected as the research objectives. And the loss series of the two indexes are tested through normality test, unit root test, autocorrelation test and ARCH effect test. The outcomes of these tests indicate these loss series are skewed and stationary with the effect of ARCH. Hereby, the GARCH-type models are suitable to be used to estimate VaR. The TGARCH model and the EGARCH model under the hypothesis of Student’s t-distribution and generalized error distribution are employed for the six test periods from 2011 to 2016. And it can be concluded with backtesting that all these four models (the VaR-TGARCH-t model, the VaR-TGARCH-GED model, the VaR-EGARCH-t model and the VaR-EGARCH-GED model) are appropriate for the two indexes despite the fact several models fail the Kupiec test for the period 2015-2016.For the Shenzhen Component index, the VaR-TGARCH-t model may fit it most because all numbers of violations for the six test periods