In this thesis, the foundations of evaluating the performance of volatility forecasting methods are explored, and a mathematical framework is created to determine the overall forecasting performance based on observed daily returns across multiple financial instruments. Multiple volatility responses are investigated, and theoretical corrections are derived under the assumption that the log returns follow a normal distribution. Performance measures that are independent of the long-term volatility profile are explored and tested. Well-established volatility forecasting methods, such as moving average and GARCH (p,q) models, are implemented and validated on multiple volatility responses. The obtained results reveal no significant difference in the performances between the moving average and GARCH (1,1) volatility forecast. However, the observed non-zero bias and a separate analysis of the distribution of the log returns reveal that the theoretically derived corrections are insufficient in correcting the not-normally distributed log returns. Furthermore, it is observed that there is a high dependency of abslute performances on the considered evaluation period, suggesting that comparisons between periods should not be made. This study is limited by the fact that the bootstrapped confidence regions are ill-suited for determining significant performance differences between forecasting methods. In future work, statistical significance can be gained by bootstrapping the difference in performance measures. Furthermore, a more in-depth analysis is needed to determine more appropriate theoretical corrections for the volatility responses based on the observed distribution of the log returns. This will increase the overall forecasting performance and improve the overall quality of the evaluation framework. / I detta arbete utforskas grunderna för utvärdering av prestandan av volatilitetsprognoser och ett matematiskt ramverk skapas för att bestämma den övergripande prestandan baserat på observerade dagliga avkastningar för flera finansiella instrument. Ett antal volatilitetsskattningar undersökts och teoretiska korrigeringar härleds under antagandet att log-avkastningen följer en normalfördelningen. Prestationsmått som är oberoende av den långsiktiga volatilitetsprofilen utforskas och testas. Väletablerare metoder för volatilitetsprognostisering, såsom glidande medelvärden och GARCH-modeller, implementeras och utvärderas mot flera volatilitetsskattningar. De erhållna resultaten visar att det inte finns någon signifikant skillnad i prestation mellan prognoser producerade av det glidande medelvärdet och GARCH (1,1). Det observerade icke-noll bias och en separat analys av fördelningen av log-avkastningen visar dock att de teoretiskt härledda korrigeringarna är otillräckliga för att fullständigt korrigera volatilitesskattningarna under icke-normalfördelade log-avkastningar. Dessutom observeras att det finns ett stort beroende på den använda utvärderingsperioden, vilket tyder på att jämförelser mellan perioder inte bör göras. Denna studie är begränsad av det faktum att de använda bootstrappade konfidensregionerna inte är lämpade för att fastställa signifikanta skillnader i prestanda mellan prognosmetoder. I framtida arbeten behövs fortsatt analys för att bestämma mer lämpliga teoretiska korrigeringar för volatilitetsskattningarna baserat på den observerade fördelningen av log-avkastningen. Detta kommer att öka den övergripande prestandan och förbättra den övergripande kvaliteten på prognoserna.

The Heston stochastic volatility model is one extension of the Black-Scholes model which describes the money markets more accurately so that more realistic prices for derivative products are obtained. From the stochastic differential equation of the underlying financial product a partial differential equation (p.d.e.) for the value function of an option can be derived. This p.d.e. can be solved with the finite difference method (f.d.m.). The stability and consistency of the method is examined. Furthermore a boundary condition is proposed to reduce the numerical error. Finally a non uniform structured grid is derived which is fairly optimal for the numerical result in the most interesting point. / Das stochastische Volatilitaetsmodell von Heston ist eines der Erweiterungen des Black-Scholes-Modells. Von der stochastischen Differentialgleichung fuer den unterliegenden Prozess kann eine partielle Differentialgleichung fuer die Wertfunktion einer Option abgeleitet werden. Es wird die Loesung mittels Finiter Differenzenmethode untersucht (Konsistenz, Stabilitaet). Weiterhin wird eine Randbedingung und ein spezielles nicht-uniformes Netz vorgeschlagen, was zu einer starken Reduzierung des numerischen Fehlers der Wertfunktion in einem ganz bestimmten Punkt fuehrt.

South Africa has become more dependent on portfolio inflow to finance investment and consumption due to the low rate of government and household savings. Therefore, it is important from South Africa‟s perspective to maintain a stable portfolio inflow in order to ensure that the current account deficit does not reach unsustainable levels. However, portfolio inflow is anything but stable in South Africa. The risk associated with this is that when foreigners‟ expectations of South Africa shift, due to any form of instability or risk within the country or even internationally, it leads to massive withdrawals or outflow of funds, which in turn causes the currency to depreciate. The portfolio balance theory on the other hand states that an increase in portfolio inflow leads to the appreciation of the nominal exchange rate, and that this is perceived to work against economic growth. The main objective of this research is to determine the nature of the relationship between exchange rate volatility and portfolio flows, and the extent to which volatility in the exchange rate affect South Africa‟s portfolio inflow. The research uses Vector Autoregressive (VAR) models and quarterly data, ranging from 1995 to 2012 to investigate this relationship. From the VAR models a Granger causality test, as well impulse response functions is used to shed light on the influence of a one-unit shock in both foreign portfolio inflow and exchange rate volatility on the other variables in the model. Exchange rate volatility is measured using both Autoregressive Conditional Heteroscedasticity (ARCH) family models and the conventional standard deviation, in order to control for possible biasness caused by the choice of instrument of volatility. The results showed the nature of the relationship between exchange rate volatility and foreign portfolio inflow to South Africa‟s capital markets can be described as country-dependent and time-varying. South Africa‟s portfolio inflow exhibits high volatility and low persistence that are characteristics normally associated with “hot money”, which is largely driven by foreign investors‟ appetite for short-term speculative gains. The study identified the consistent presence of bidirectional causality between the exchange rate volatility and foreign portfolio inflow to South Africa, irrespective of the measurement of exchange rate volatility. The results also revealed that net portfolio flows are associated with exchange rate appreciation and that foreign portfolio inflow react much stronger to changes in exchange rate volatility than vice versa. / MCom (Risk Management), North-West University, Potchefstroom Campus, 2015

South Africa has become more dependent on portfolio inflow to finance investment and consumption due to the low rate of government and household savings. Therefore, it is important from South Africa‟s perspective to maintain a stable portfolio inflow in order to ensure that the current account deficit does not reach unsustainable levels. However, portfolio inflow is anything but stable in South Africa. The risk associated with this is that when foreigners‟ expectations of South Africa shift, due to any form of instability or risk within the country or even internationally, it leads to massive withdrawals or outflow of funds, which in turn causes the currency to depreciate. The portfolio balance theory on the other hand states that an increase in portfolio inflow leads to the appreciation of the nominal exchange rate, and that this is perceived to work against economic growth. The main objective of this research is to determine the nature of the relationship between exchange rate volatility and portfolio flows, and the extent to which volatility in the exchange rate affect South Africa‟s portfolio inflow. The research uses Vector Autoregressive (VAR) models and quarterly data, ranging from 1995 to 2012 to investigate this relationship. From the VAR models a Granger causality test, as well impulse response functions is used to shed light on the influence of a one-unit shock in both foreign portfolio inflow and exchange rate volatility on the other variables in the model. Exchange rate volatility is measured using both Autoregressive Conditional Heteroscedasticity (ARCH) family models and the conventional standard deviation, in order to control for possible biasness caused by the choice of instrument of volatility. The results showed the nature of the relationship between exchange rate volatility and foreign portfolio inflow to South Africa‟s capital markets can be described as country-dependent and time-varying. South Africa‟s portfolio inflow exhibits high volatility and low persistence that are characteristics normally associated with “hot money”, which is largely driven by foreign investors‟ appetite for short-term speculative gains. The study identified the consistent presence of bidirectional causality between the exchange rate volatility and foreign portfolio inflow to South Africa, irrespective of the measurement of exchange rate volatility. The results also revealed that net portfolio flows are associated with exchange rate appreciation and that foreign portfolio inflow react much stronger to changes in exchange rate volatility than vice versa. / MCom (Risk Management), North-West University, Potchefstroom Campus, 2015

With few previous data and literature based on the South African banking sector, the key aim of this study was to contribute further results concerning the effect of operational loss events on the reputation of South African banks. The main distinction between this study and previous empirical research is that a small sample of South African banks listed on the JSE, between 2000 and 2014 was used. Insurance companies fell outside the scope of the study. The study primarily focused on identifying reputational risk among Regal Treasury Bank, Saambou Bank, African Bank and Standard Bank. The events announced by these banks occurred between 2000 and 2014. The precise date of the announcement of the operational events was also determined. Stock price data were collected for those banks that had unanticipated operational loss announcements (i.e. the event). Microsoft Excel models applied to the reputational loss as the difference between the operational loss announcement and the loss in the stock returns of the selected banks. The results indicated significant negative abnormal returns on the announcement day for three of the four banks. For one of the banks it was assumed that the operational loss was not significant enough to cause reputational risk. The event methodology similar to previous literature, furthermore examined the behaviour of return volatility after specific operational loss events using the sample of banks. The study further aimed at making two contributions. Firstly, to analyse return volatility after operational loss announcements had been made among South African banks, and secondly, to compare the sample of affected banks with un-affected banks to further identify whether these events spilled over into the banking industry and the market. The volatility of these four banks were compared to three un-affected South African banks. The results found that the operational loss events for Regal Treasury Bank and Saambou Bank had no influence on the unaffected banks. However the operational loss events for African Bank and Standard Bank influenced the sample of unaffected banks and the Bank Index, indicating systemic risk.

With few previous data and literature based on the South African banking sector, the key aim of this study was to contribute further results concerning the effect of operational loss events on the reputation of South African banks. The main distinction between this study and previous empirical research is that a small sample of South African banks listed on the JSE, between 2000 and 2014 was used. Insurance companies fell outside the scope of the study. The study primarily focused on identifying reputational risk among Regal Treasury Bank, Saambou Bank, African Bank and Standard Bank. The events announced by these banks occurred between 2000 and 2014. The precise date of the announcement of the operational events was also determined. Stock price data were collected for those banks that had unanticipated operational loss announcements (i.e. the event). Microsoft Excel models applied to the reputational loss as the difference between the operational loss announcement and the loss in the stock returns of the selected banks. The results indicated significant negative abnormal returns on the announcement day for three of the four banks. For one of the banks it was assumed that the operational loss was not significant enough to cause reputational risk. The event methodology similar to previous literature, furthermore examined the behaviour of return volatility after specific operational loss events using the sample of banks. The study further aimed at making two contributions. Firstly, to analyse return volatility after operational loss announcements had been made among South African banks, and secondly, to compare the sample of affected banks with un-affected banks to further identify whether these events spilled over into the banking industry and the market. The volatility of these four banks were compared to three un-affected South African banks. The results found that the operational loss events for Regal Treasury Bank and Saambou Bank had no influence on the unaffected banks. However the operational loss events for African Bank and Standard Bank influenced the sample of unaffected banks and the Bank Index, indicating systemic risk.

För att prissätta optioner är val av modell en viktig fråga. I denna kandidatuppsats beskrivs både Black & Scholes modell och SABR-modellen. Förstnämnda modell är enklare än SABR-modellen men bygger på antaganden som inte stämmer överens med verkligheten. Den ger heller inte någon explicit formel för den implicita volatiliteten och predikterar inte heller på ett korrekt sätt fenomenet volatility smile vilket observeras på marknaden. Syftet med uppsatsen är att utvärdera prestandan hos SABR-modellen och användarvänligheten, samt att undersöka lite av teorin bakom modellen och vissa av dess egenskaper. Till grund för beräkningarna ligger datamaterial hämtat från Nasdaq OMX Nordic. Enligt mina beräkningar är resultatet att SABR-modellen endast presterar marginellt bättre än Black & Scholes-modellen. Dock kan även små förbättringar spela stor roll i dessa sammanhang.

This research assessed market efficiency, volatility behaviour, asset pricing, and oil price risk exposure of the oil and gas companies quoted on the London Stock Exchange with the aim of providing fresh evidence on the pricing dynamics in this sector. In market efficiency analysis, efficient market hypothesis (EMH) and random walk hypothesis were tested using a mix of statistical tools such as Autocorrelation Function, Ljung-Box Q-Statistics, Runs Test, Variance Ratio Test, and BDS test for independence. To confirm the results from these parametric and non-parametric tools, technical trading and filter rules, and moving average based rules were also employed to assess the possibility of making abnormal profit from the stocks under study. In seasonality analysis, stock returns were tested for the day-of-the-week and month-of-the-year effects. Volatility processes, estimation, and forecasting were undertaken using both asymmetric and symmetric volatility models such as GARCH (1,1) and Threshold ARCH or TARCH (1,1,1) to investigate the volatility behaviour of stock returns. To determine the effect of an exogenous variable on volatility, Brent crude oil price was used in the models formulated as a variance regressor for the assessment of its impact on volatility. The models were then used to forecast the price volatility taking note of the forecasting errors for the determination of the most effective forecasting model. International oil price risk exposure of the oil and gas sector was measured using a multi-factor asset pricing model similar to that developed by Fama and French (1993). Factors used in the asset pricing model are assessed for statistical significance and relevance in the pricing of oil and gas stocks. Data used in the study were mainly the adjusted daily closing prices of oil and gas companies quoted on the exchange. Five indices of FTSE All Share, FTSE 100, FTSE UK Oil and Gas, FTSE UK Oil and Gas Producers, and FTSE AIM SS Oil and Gas were also included in the analysis. Our findings suggest that technical trading rules cannot be used to gain abnormal returns, which could be regarded as a sign for weak form market efficiency. The results from seasonality analysis have not shown any day-of-the-week or monthly effect in stock returns. The pattern of stock returns’ volatility can be estimated and forecasted, although the relationship between risk and return cannot be generalised. On a similar note, the relationship between volatility attributes and the efficient market hypothesis cannot be clearly established. However, we have established that volatility modelling can significantly measure the quantum of risk in the oil and gas sector. Market risk, oil price risk, size and book-to-market related factors in asset pricing models were found to be relevant in the determination of asset prices of the oil and gas companies.

What are the main macroeconomic factors that help understand economic growth in Brazil since 1870? Are institutions (and changes in institutions) a deep cause of economic growth in Brazil? Are these effects fundamentally and systematically different? Does the intensity and the direction (the sign) of these effects vary over time, in general and, in particular, do they vary with respect to short- versus long-run considerations? This thesis tries to answer these questions focusing on within country over long periods of time. It uses the power-ARCH (PARCH) econometric framework with annual time series from 1870 to 2003. The results suggest that financial development (domestic and international) exhibit the most robust first-order effects on growth and its volatility. Political instability, trade openness and public deficit play important yet secondary roles since the effects of the first two do not extent to the long-run (that is, they are restricted to the short-run) and those off the latter are sensitive to the measures of the variables used in our analysis.

The aim of this thesis is a development of a new class of financial models with random parameters, which are computationally efficient and have the same level of performance as existing ones. In particular, this research is threefold. I have studied the evolution of storable commodity and commodity futures prices in time using a new random parameter model coupled with a Kalman filter. Such a combination allows one to forecast arbitrage-free futures prices and commodity spot prices one step ahead. Another direction of my research is a new volatility model, where the volatility is a random variable. The main advantage of this model is high calibration speed compared to the existing stochastic volatility models such as the Bates model or the Heston model. However, the performance of the new model is comparable to the latter. Comprehensive numerical studies demonstrate that the new model is a very competitive alternative to the Heston or the Bates model in terms of accuracy of matching option prices or computing hedging parameters. Finally, a new futures pricing model for electricity futures prices was developed. The new model has a random volatility parameter in its underlying process. The new model has less parameters, as compared to two-factor models for electricity commodity pricing with and without jumps. Numerical experiments with real data illustrate that it is quite competitive with the existing two-factor models in terms of pricing one step ahead futures prices, while being far simpler to calibrate. Further, a new heuristic for calibrating two-factor models was proposed. The new calibration procedure has two stages, offline and online. The offline stage calibrates parameters under a physical measure, while the online stage is used to calibrate the risk-neutrality parameters on each iteration of the particle filter. A particle filter was used to estimate the values of the underlying stochastic processes and to forecast futures prices one step ahead. The contributory material from two chapters of this thesis have been submitted to peer reviewed journals in terms of two papers: • Chapter 4: “A fast calibrating volatility model” has been submitted to the European Journal of Operational Research. • Chapter 5: “Electricity futures price models : calibration and forecasting” has been submitted to the European Journal of Operational Research.