This study attempts to quantify the shocks to a banking network and analyze the transfer of shocks through the network. We consider two sources of shocks: external shocks due to market and macroeconomic factors which impact the entire banking system, and idiosyncratic shocks due to failure of a single bank. The external shocks will be estimated by using two methods: (i) non-parametric simulation of the time series of shocks that occurred to the banking system in the past, and (ii) using the extreme value theory (EVT) to model the tail part of the shocks. The external shocks we considered in this study are due to exchange rate and treasury bill rate volatility. Also, an ARMA/GARCH model is used to extract iid residuals for this purpose. In the next step, the probability of the failure of banks in the system is studied by using Monte Carlo simulation. We calibrate the model such that the network resembles the Canadian banking system.

The statements that include sufficient detail to identify the probability distributions of future prices are asset price dynamics. In this research, using the empirical methods that could explain the historical prices and discuss about how prices change we investigate various important characteristics of the dynamics of asset pricing. The volatility changes can explain very important facts about the asset returns. Volatility could gauge the variability of prices over time. In order to do the volatility modelling we use the conditional heteroskedasticitc models. One of the most powerful tools to do so is using the idea of autoregressive conditional heteroskedastic process or ARCH models, which fill the gap in both academic and practical literature. In this work we detect the asymmetric volatility effect and investigate long memory properties in volatility in Canadian stock market index, using daily data from 1979 through 2015. On one hand, we show that there is an asymmetry in the equity market index. This is an important indication of how information impacts the market. On the other hand, we investigate for the long-range dependency in volatility and discuss how the shocks are persistence. By using the long memory-GARCH models, we not only take care of both short and long memory, but also we compute the d parameter that stands for the fractional decay of the series. By considering the breaks in our dataset, we compare our findings on different conditions to find the most suitable fit. We present the best fit for GARCH, EGARCH, APARCH, GJR-GARCH, FIGARCH, FIAPARCH, and FIEGARCH models.

Diplomová práce se zabývá modifikovaným IS-MP-IA modelem české ekonomiky rozšířeným o veličiny týkající se EU. Model zachycuje vliv eknomiky EU na ekonomický vývoj ČR a umožňuje snadno interpretovat dopady prováděné měnové a fiskální politiky. Lze říci, že použitá GARCH metoda je vhodná pro odhad modifikovaného IS-MP-IA modelu a pro následnou predikci.

Ingeniero Civil Electricista / En el presente informe se da cuenta del proceso de diseño e implementación de una metodología para la predicción de niveles de volatilidad de retornos financieros basada en modelos de volatilidad estocástica, sensibles al riesgo, y con entrada exógena. Dicha metodología se basa en modelos generalizados de heterocedasticidad condicional autoregresiva (GARCH por sus siglas en inglés), los que consideran que los retornos de activos financieros pueden ser explicados por información pasada, complementada con un proceso de innovación. En particular se utilizará el denominado modelo \emph{unobserved} GARCH (uGARCH), el que considera que es un proceso de innovación no observado que maneja la evolución de volatilidad en función del tiempo, implementado mediante un enfoque de filtrado Bayesiano sensible al riesgo que logra identificar periodos de alta volatilidad y relacionar dichos periodos con fenómenos que se observan posteriormente en indicadores de otros husos horarios. Para validar el modelo propuesto con datos reales se buscan indicadores de mercados que sean de relación cercana, pero que contengan una diferencia horaria significativa; como es el caso de los mercados asiático y latinoamericano, ya que tienen la mayor diferencia horaria posible y los principales países componentes mantienen una estrecha relación comercial. En efecto entre otras características, China es el mayor socio comercial para la venta de hierro Brasileño, por lo que información fundamental de sus variables macroeconómicas impactan en la valoración de ambos mercados. Finalmente el resultado de la implementación indica que para periodos de aumento de volatilidad en mercados emergentes latinoamericanos (representados con el índice MSCI LA), la predicción con filtro de partículas sensible al riesgo con entrada exógena dependiente del índice asiatico (MSCI ASIAXJ), es superior a la predicción del filtro de partículas clásico bajo los valores calculados de los indicadores propuestos, que además se evidencia gráficamente. En efecto, el valor del índice de predicción calculado en la muestra completa, es 50\% más favorable para el método propuesto, que el filtro de partículas clásico, diferencia que se hace aún más significativa cuando el efecto de la entrada exógena es relevante, llegando a ser 16 veces superior en ese caso.

Prior research has established that idiosyncratic volatility of the securities prices exhibits a positive trend. This trend and other factors have made the merits of investment diversification and portfolio construction more compelling. A new optimization technique, a greedy algorithm, is proposed to optimize the weights of assets in a portfolio. The main benefits of using this algorithm are to: a) increase the efficiency of the portfolio optimization process, b) implement large-scale optimizations, and c) improve the resulting optimal weights. In addition, the technique utilizes a novel approach in the construction of a time-varying covariance matrix. This involves the application of a modified integrated dynamic conditional correlation GARCH (IDCC - GARCH) model to account for the dynamics of the conditional covariance matrices that are employed. The stochastic aspects of the expected return of the securities are integrated into the technique through Monte Carlo simulations. Instead of representing the expected returns as deterministic values, they are assigned simulated values based on their historical measures. The time-series of the securities are fitted into a probability distribution that matches the time-series characteristics using the Anderson-Darling goodness-of-fit criterion. Simulated and actual data sets are used to further generalize the results. Employing the S&P500 securities as the base, 2000 simulated data sets are created using Monte Carlo simulation. In addition, the Russell 1000 securities are used to generate 50 sample data sets. The results indicate an increase in risk-return performance. Choosing the Value-at-Risk (VaR) as the criterion and the Crystal Ball portfolio optimizer, a commercial product currently available on the market, as the comparison for benchmarking, the new greedy technique clearly outperforms others using a sample of the S&P500 and the Russell 1000 securities. The resulting improvements in performance are consistent among five securities selection methods (maximum, minimum, random, absolute minimum, and absolute maximum) and three covariance structures (unconditional, orthogonal GARCH, and integrated dynamic conditional GARCH).

With the acceleration of economic globalization, the immature Chinese mainland stock market is gradually associated with the stock markets of other countries. This paper predict the return rate of Chinese mainland stock market using several models from GARCH family, test the predictability by calculating Value-at-Risk, also capture the dynamic correlation between other fifive countries or region and mainland China by DCC-GARCH model. The results indicate that E-ARMA-GARCH model fifits the best due to the signifificant heteroscedasticity and leverage effect of Chinese mainland stock market. It has the strongest positive correlation with HongKong while the weakest correlation with the United States.

This master thesis deals with the modeling of multivariate volatility in finan- cial time series. The aim of this work is to describe in detail selected approaches to modeling multivariate financial volatility, including verification of models, and then apply them in an empirical study of asset portfolio optimization. The results are compared with the classical approach of portfolio optimization theory based on unconditional moment estimates. The evaluation was based on four known op- timization problems, namely minimization of variance, Markowitz's model, ma- ximization of the Sharpe ratio and minimization of CVaR. The output portfolios were compared by using four metrics that reflect the returns and risks of the port- folios. The results demonstrated that employing the multivariate volatility models one obtains higher expected returns with less expected risk when comparing with the classical approach. 1

Asset pricing models such as the CAPM calls for the estimation of beta as a measure of the systematic risk. Using historical betas as an input to portfolio analysis requires the assumption of beta stationarity. The existing literature on beta dynamics suggest a somewhat high dispersion of the beta persistence across stocks. In previously unexplored territory, this study aims to investigate factors associated with the degree of beta persistence. By using a sample of 237 U.S. stocks with daily returns observed over the period 1984 to 2015, yearly stock betas were estimated using a GARCH / Maximum Likelihood framework. Autocorrelation properties of these beta series was then crosssectionally regressed on five hypothesized determining variables. Product type as well as the absolute value of beta was found to have a significant effect on the first-order autocorrelation of beta.

The low-volatility anomaly can be described as the unexpected outperformance of low-volatility stocks compared to high-volatility stocks over the long-term. This dissertation investigates the low-volatility anomaly and its presence on the Johannesburg Stock Exchange (JSE). Possible reasons behind why low-volatility stocks consistently outperform their high volatility counterparts, as well as their own expected return, over the long-term are discussed. This includes analysing how financial risk is measured and whether this plays a role in obscuring the expected risk-return relationship, in addition to other fundamental factors impacting expected returns. It is found that the low-volatility anomaly is present on the JSE and that using a number of different risk metrics does not significantly change where a stock is ranked on the risk spectrum. Additionally, including an interest rate exposure factor, a value factor and a momentum factor lowers the unexpected portion (Alpha) of the returns of low volatility stocks, at the same time as narrowing the gap between the unexpected performance of the lowest and highest volatility stocks.

The thesis concerns the topic of forecasting using Neural Networks, particu- larly the return and volatility forecasting in the volatile period of Covid-19. The thesis uses adjusted close daily data from Jan 1, 2000, until Jan 1, 2021, of the S&P index and Prague Exchange Stock index (PX). The comparison was between the vanilla econometrical model, a neural network model, and a hybrid neural network model. Hybrid neural networks were constructed with an additional feature column of the fitted econometrical model. Additionally to comparing the prediction, a risk-return trade-o analysis of the forecasted series was conducted. The test period for all models was from Jan 1, 2020, until Jan 1, 2021, where predictions were made. During the test period, MSE be- tween predicted and true values was extracted and compared. The results are that the hybrid model outperformed both econometrical as well as only neural networks models. Furthermore, the risk-return trade-o forecast provided by the hybrid model fares better than the other ones. JEL Classification C53, C81 Keywords Financial Time Series, Forecasting, Neural Net- works, ARIMA, GARCH Title Forecasting with Neural Network during Covid- 19 Crisis Author's e-mail tiep.luud@gmail.com Supervisor's e-mail barunik@fsv.cuni.cz