[pt] Realizar a previsão de volatilidade futura é algo que intriga muitos estudiosos, pesquisadores e pessoas do mercado financeiro. O modelo e a metodologia utilizados no cálculo são fundamentais para o apreçamento de opções e dependendo das variáveis utilizadas, o resultado se torna muito sensível, propiciando resultados diferentes. Tudo isso pode causar cálculos imprecisos e estruturação de estratégias erradas de compra e venda de ações e opções por empresas e investidores. Por isso, o objetivo deste trabalho é utilizar alguns modelos para o cálculo de volatilidade futura e analisar os resultados, avaliando qual o melhor modelo a ser empregado, propiciando uma melhor previsão da volatilidade futura. / [en] Make a prediction of future volatility is a subject that causes debate between scholars, researchers and people in the financial market. The modeal nd methodology used in the calculation are fundamental to the pricing of options and depending on the variables used, the result becomes very sensitive, giving different results. All this can cause inaccurate calculations and wrong strategies for buying and selling stocks and options by companies and investors. Therefore, the objective of this work is to use models for the calculation of future volatility and analyze the results, evaluating the best model to be used, allowing a better prediction of future volatility.

This research aims to examine if a negative relationship exists between the dividend yield and stock price volatility of firms listed on the Swedish Stock exchange market, which is of utter interest and intrinsic for investors and financial analyst in the process of valuing a security’s and a stock portfolio's risk and return. The data that was utilized for this study consists of 52 companies for the period of 2010 to 2019 which makes up for 520 observations. A pooled regression model and a multiple ordinary least squares model was applied to test the relationship. The results show a negative relationship between the dividend yield and stock price volatility. On the other hand, the results indicate that there is a significant positive relationship between earnings volatility and stock price volatility. However, there is a negative relationship for leverage, market value and asset growth with stock price volatility.

Volatility modelling is a field dominated by classic Econometric methods such as the Nobel Prize winning Autoregressive conditional heteroskedasticity (ARCH) model. This paper therefore investigates if the field of Deep Learning can live up to the hype and outperform classic Econometrics in forecasting of realized volatility. By letting the Heterogeneous AutoRegressive model of Realized Volatility with multiple jump components (HAR-RV-CJ) represent the Econometric field as benchmark model, we compare its efficiency in forecasting realized volatility to four Deep Learning models. The results of the experiment show that the HAR-RV-CJ performs in line with the four Deep Learning models: Feed Forward Neural Network (FNN), Recurrent Neural Network (RNN), Long Short Term Memory network (LSTM) and Gated Recurrent Unit Network (GRU). Hence, the paper cannot conclude that the field of Deep Learning is superior to classic Econometrics in forecasting of realized volatility.

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.

In this thesis, we study the return and volatility spillovers between forex and stock markets in Scandinavian countries employing recently developed method- ology of spillover indices. Those measures are based on forecast error variance decomposition of generalized vector autoregressive (GVAR) model. This allows us to estimate both total and directional spillovers. Moreover, frequency connect- edness analysis is conducted by decomposing the spillover indices into frequency bands, corresponding to short-, medium- and long-run connectedness. We used daily data for major stock market indices and exchange rates of domestic cur- rency towards US dollar for Norway, Sweden, Denmark and Finland. Our data spans from February 2002 till July 2018 that covers turmoil periods of global fi- nancial crisis in 2007-2009, European sovereign debt crisis 2010-2013 and Brexit referendum in mid 2016. Our empirical analysis reveals that Norwegian financial markets do not contribute much to both return and volatility spillovers. On the other hand, euro and Danish FX market perform very similarly, by exhibiting the highest spillover contributions for both returns and volatility. Furthermore, distinct increasing trends in spillovers are revealed during the turmoil periods for most of the markets. From frequency...

Nowadays, there is a wide range of forecasting methods and forecasters encounter several challenges during selection of an optimal method for volatility forecasting. In order to make use of wide selection of forecasts, this thesis tests multiple forecast combination methods. Notwithstanding, there exists a plethora of forecast combination literature, combination of traditional methods with machine learning methods is relatively rare. We implement the following combination techniques: (1) simple mean forecast combination, (2) OLS combination, (3) ARIMA on OLS combined fit, (4) NNAR on OLS combined fit and (5) KNN regression on OLS combined fit. To our best knowledge, the latter two combination techniques are not yet researched in academic literature. Additionally, this thesis should help a forecaster with three choice complication causes: (1) choice of volatility proxy, (2) choice of forecast accuracy measure and (3) choice of training sample length. We found that squared and absolute return volatility proxies are much less efficient than Parkinson and Garman-Klass volatility proxies. Likewise, we show that forecast accuracy measure (RMSE, MAE or MAPE) influences optimal forecasts ranking. Finally, we found that though forecast quality does not depend on training sample length, we see that forecast...

<div>We develop a growth option and asset pricing model that incorporates uncertain cash flow volatility by way of a bounded quadratic diffusion. Using different measures of risk uncertainty, we study the combined effects of risk and its associated uncertainty on project values, firm investment, and the resulting returns. Uncertain cash flow volatility is modeled by a Jacobi process, and our main interest is the effect of the max uncertainty arising from the diffusion term. For comparison, we also model the volatility by a CIR process. In regards to the Jacobi process, we consider upper and lower bounds on cash flow volatility as measures of uncertainty. For the max uncertainty and upper bound, we find that higher uncertainty leads to less investment, higher returns, and lower project values. In the case of the lower bound, we find that higher uncertainty leads to more investment, lower returns, and higher project values. Comparatively, using a CIR process in place of the Jacobi process yields differences in returns and growth option values, showing the importance of the diffusion term in the volatility process. Finally, we have reduced the computational complexity of the simulation. This allows the user to generate long time series and run cross sectional regressions with many firms.</div>

The rise of social media and the “retail investor” has completely shifted the investing landscape. A new paradigm has been created where people have easier access than ever to invest in the stock market from the convenience of their phones. This is accomplished through zero-commission trading apps, like Robinhood, meaning less starting capital is required. This research is used to investigate the relationship between the frequency of social media mentions on Twitter and a particular stock’s volatility. It is hypothesized that Twitter mentions will affect stock volatility. This will be done using the qualitative data analyzing tool AtlasTi to calculate the frequency in which a particular stock ticker is mentioned on Twitter during trading hours. Using AtlasTi, the number of mentions for twenty-eight individual stocks was monitored twice a day for twenty total trading days, or approximately one month. This resulted in forty individual time frames of data, or 1,120 total data points. The volatility of the stock will then be calculated using data from Yahoo! Finance. Using panel data analysis, the number of stock mentions on Twitter will be cross-checked with the volatility of the correlating stock under the same time period to evaluate the relationship between the two variables. While our final analysis has not yet been calculated, it is expected that our results will show a relationship between heavily mentioned stocks and increased volatility. It is intended that our research will aid future investors when making decisions on how to invest in assets heavily mentioned on social media.

In this dissertation, the price of variance swaps under stochastic volatility models based on the work done by Barndorff-Nielsen and Shepard (2001) and Heston (1993) is discussed. The choice of these models is as a result of properties they possess which position them as an improvement to the traditional Black-Scholes (1973) model. Furthermore, the popularity of these models in literature makes them particularly attractive. A lot of work has been done in the area of pricing variance swaps since their inception in the late 1990’s. The growth in the number of variance contracts written came as a result of investors’ increasing need to be hedged against exposure to future variance fluctuations. The task at the core of this dissertation is to derive closed or semi-closed form expressions of the fair price of variance swaps under the two stochastic models. Although various researchers have shown that stochastic models produce close to market results, it is more desirable to obtain the fair price of variance derivatives using models under which no assumptions about the dynamics of the underlying asset are made. This is the work of a useful analytical formula derived by Demeterfi, Derman, Kamal and Zou (1999) in which the price of variance swaps is hedged through a finite portfolio of European call and put options of different strike prices. This scheme is practically explored in an example. Lastly, conclusions on pricing using each of the methodologies are given. / Dissertation (MSc)--University of Pretoria, 2019. / Mathematics and Applied Mathematics / MSc (Financial Engineering) / Unrestricted

Volcanoes are a key component of the Earth system, with volcanic activity reaching from deep in the Earth’s mantle and extending to interactions with volcanic gases and the atmosphere. Volatile trace metals degas from volcanic eruptions and at fumaroles, but their behaviour is poorly understood. I designed and built a benchtop fumarole, from which I degassed a silicate melt with trace metals, to simulate the volatilization and sublimation of trace metals from volcanic gases. I collected sublimates along a temperature gradient to examine the behaviour of the trace metals. The experimental sublimates were analysed for their chemical composition and phase identification. Lithium, Cu, As, Rb, Mo, Ag, Cd, Cs, W, Pt, Tl, Pb and Bi were found to be volatile and sublimed in elevated concentrations at various temperatures between 250-600°C. Compared to natural fumarole studies, similar volatile behaviour is seen for Cu, As, Ag and Tl. Variability between the experimental and natural fumarole sublimates is proposed to be from a lack of ligands in the experiments. Ligands can complex with trace metals, to transport and sublime mineralogical phases. Given the importance of ligands to metal complexation, I proceeded to examine the importance of chloride as a ligand in volatile transport and sublimation of trace metals. I degassed a silicate melt with trace metals and variable concentrations of Cl-, up to 2 wt% Cl-, in air. Sublimates produced from these experiments were analysed for mineralogical and chemical information. Raman spectroscopy and scanning electron microscopy helped to determine that silica polymorphs occur at all temperatures and that halite forms below 600°C. Additional phases, including hydrated phases transporting Mo, Cu and Pb also formed as sublimates. These hydrated phases are suggested to be hydrated post-experiment or are Cl--bearing analogues. The addition of Cl- to the experiments increases the concentration of Li, Rb, Cs, Ag, Cr, Cu, Mo and W in the sublimates compared to Cl-free experiments and Cl-bearing phases are likely hosts of volatile trace metals. Volcanic gases in nature do not have the oxygen fugacity of air and contain considerable S. To conduct sublimation experiments at various lower oxygen fugacities and with S as it is a redox sensitive ligand, I adapted my original benchtop fumarole design to a gas-mixing furnace, in which I degassed silicate melts containing S, Cl and trace metals. Substantial loss of S and Zn, Sn, As, Bi, Pb and Cd occurred from the starting material melt in the most reduced experiment at 4.6 log units below the FMQ buffer. This loss corresponded to increased concentrations of the same elements in the sublimates of the same experiment. These trace elements are likely hosted as sulfide minerals, as the fO2 conditions are in the sulfide stability field. This agrees with thermodynamic calculations that determine that sulfides should be stable in similar conditions to this experiment. Chlorides are sublimed in experiments from ~200-650°C and are likely subliming as a NaCl-KCl-FeCl3 solid solution. Halite is calculated to form at all temperatures in the experiments, based on modelling. These chlorides are probably hosting Cu, Cd, Bi, Li, Rb and Ag in the experiments. In nature, if these metals are in soluble salts, when leached they provide a source of metals to the environment where they are deposited. Overall, I demonstrated that trace metal behaviour in the sublimates from volcanic gases will be affected by available ligands and the oxygen fugacity of the melt and the gas. Chlorides are a likely phase to host trace metals and are ubiquitous in experiments, even with variable melt compositions, fO2 conditions and across a wide temperature range. / Graduate