Contributions to model risk

[no abstract

Estimation of value-at-risk and expected shortfall using copulas

Includes bibliographical references (leaves 76-77)

Measuring Systemic Risk in the European Banking Sector: A copula CoVar approach

We propose a new methodology based on copula functions to estimate CoVaR, the Valueat-Risk (VaR) of the financial system conditional on an institution being under financial distress. Our Copula CoVaR approach provides simple, closed-form expressions for various definitions of CoVaR for a broad range of copula families and allows the CoVaR of an institution to have time-varying exposure to its VaR. We extend this approach to estimate other “co-risk” measures such as Conditional Expected Shortfall (CoES). We focus on a portfolio of large European banks and examine the existence of common market factors triggering systemic risk episodes. Further, we analyse the extent to which bank-specific characteristics such as size, leverage, and equity beta are associated with institutions’ contribution to systemic risk and highlight the importance of liquidity risk at the outset of the financial crisis in summer 2007. Finally, we investigate the link between macroeconomy and systemic risk and find that changes in major macroeconomic variables can contribute significantly to systemic risk

Estimating Dependences and Risk between Gold Prices and S&P500: New Evidences from ARCH,GARCH, Copula and ES-VaR models

This thesis examines the correlations and linkages between the stock and commodity in order to quantify the risk present for investors in financial market (stock and commodity) using the Value at Risk measure. The risk assessed in this thesis is losses on investments in stock (S&P500) and commodity (gold prices). The structure of this thesis is based on three empirical chapters. We emphasise the focus by acknowledging the risk factor which is the non-stop fluctuation in the prices of commodity and stock prices. The thesis starts by measuring volatility, then dependence which is the correlation and lastly measure the expected shortfalls and Value at risk (VaR). The research focuses on mitigating the risk using VaR measures and assessing the use of the volatility measures such as ARCH and GARCH and basic VaR calculations, we also measured the correlation using the Copula method. Since, the measures of volatility methods have limitations that they can measure single security at a time, the second empirical chapter measures the interdependence of stock and commodity (S&P500 and Gold Price Index) by investigating the risk transmission involved in investing in any of them and whether the ups and downs in the prices of one effect the prices of the other using the Time Varying copula method. Lastly, the third empirical chapter which is the last chapter, investigates the expected shortfalls and Value at Risk (VaR) between the S&P500 and Gold prices Index using the ES-VaR method proposed by Patton, Ziegel and Chen (2018). Volatility is considered to be the most popular and traditional measure of risk. For which we have used ARCH and GARCH model in our first empirical chapter. However, the problem with volatility is that it does not take into account the direction of an investments’ movement: volatility of stocks is that they suddenly jump higher and investors are not distressed with gains. When we talk about investors for them the risk is about the odds of losing money, after my research and findings VaR is based on the common-sense fact. Hence, investors care about the odds of big losses, VaR answers the question, what is my worst-case scenario? Or simply how much I could lose in a really bad month? The results of the thesis demonstrated that measuring volatility (ARCH GARCH) alone was not sufficient in measuring the risk involved in an investment therefore methodologies such as correlation and VAR demonstrates better results. In terms of measuring the interdependence, the Time Varying Copula is used since the dynamic structure of the de- pendence between the data can be modelled by allowing either the copula function or the dependence parameter to be time varying. Lastly, hybrid model further demonstrates the average return on a risky asset for which Expected Shortfall (ES) along with some quantile dependence and VaR (Value at risk) is utilised. Basel III Accord which is applied in coming years till 2019 focuses more on ES unlike VaR, hence there is little existing work on modelling ES. The thesis focused on the results from the model of Patton, Ziegel and Chen (2018) which is based on the statistical decision theory. Patton, Ziegel and Chen (2018), overcame the problem of elicitability for ES by using ES and VaR jointly and propose the new dynamic model of risk measure. This research adds to the contribution of knowledge that measuring risk by using volatility is not enough for measuring risk, interdependence helps in measuring the dependency of one variable over the other and estimations and inference methods proposed by Patton, Ziegel and Chen (2018) using simulations proposed in ES-VaR model further concludes that ARCH and GARCH or other rolling window models are not enough for determining the risk forecasts. The results suggest, in first empirical chapter we see volatility between Gold prices and S&P500. The second empirical chapter results suggest conditional dependence of the two indexes is strongly time varying. The correlation between the stock is high before 2008. The results further displayed slight stronger bivariate upper tail, which signifies that the conditional dependence of the indexes is influence by positive shocks. The last empirical chapter findings proposed that measuring forecasts using ES-Var model proposed by Patton, Ziegel and Chen (2018) does outer perform forecasts based on univariate GARCH model. Investors want to 10 protect themselves from high losses and ES-VaR model discussed in last chapter would certainly help them to manage their funds properly

Volatility and asymmetric dependence in Central and East European stock markets

We study the effects of contagion around the global financial crisis (GFC) and the Eurozone crisis periods using German and UK returns, each paired with returns from Central and East European (CEE) stock markets that recently joined the European Union (EU). Using bivariate vector error-correction models (VECMs) estimated in GARCH(1,1), we find strong support for long-run equilibrium conditions. This finding suggests that tests of tail dependence using differenced VARs may be mis-specified when long-run equilibrium conditions apply. Past news has more persistence on current volatility in CEE markets than in the developed markets. Past volatility has more persistence in the developed markets compared to the CEE markets. The T-V symmetrized Joe–Clayton (T-V SJC) copula outperforms all other copulas in goodness-of-fit, including, the T-V Gaussian and Student t copulas. This result is supported by a differenced VAR-GARCH (1,1). For CEE and developed market returns, no more than half of our market pairs exhibit significant increases in lower tail dependence, under the T-V SJC copula. Given the number of paired comparisons, the evidence on joint extreme dependence is weak. As such, CEE stock markets experienced little contagion effects during the GFC and Eurozone crisis periods, contrary to prior results. We find that the legal environment negatively impacts financial development, perhaps causing CEE and the EU markets to be isolated

The GARCH-EVT-Copula model and simulation in scenario-based asset allocation

Financial market integration, in particular, portfolio allocations from advanced economies to South African markets, continues to strengthen volatility linkages and quicken volatility transmissions between participating markets. Largely as a result, South African portfolios are net recipients of returns and volatility shocks emanating from major world markets. In light of these, and other, sources of risk, this dissertation proposes a methodology to improve risk management systems in funds by building a contemporary asset allocation framework that offers practitioners an opportunity to explicitly model combinations of hypothesised global risks and the effects on their investments. The framework models portfolio return variables and their key risk driver variables separately and then joins them to model their combined dependence structure. The separate modelling of univariate and multivariate (MV) components admits the benefit of capturing the data generating processes with improved accuracy. Univariate variables were modelled using ARMA-GARCH-family structures paired with a variety of skewed and leptokurtic conditional distributions. Model residuals were fit using the Peaks-over-Threshold method from Extreme Value Theory for the tails and a non-parametric, kernel density for the interior, forming a completed semi-parametric distribution (SPD) for each variable. Asset and risk factor returns were then combined and their dependence structure jointly modelled with a MV Student t copula. Finally, the SPD margins and Student t copula were used to construct a MV meta t distribution. Monte Carlo simulations were generated from the fitted MV meta t distribution on which an out-of-sample test was conducted. The 2014-to-2015 horizon served to proxy as an out-of-sample, forward-looking scenario for a set of key risk factors against which a hypothetical, diversified portfolio was optimised. Traditional mean-variance and contemporary mean-CVaR optimisation techniques were used and their results compared. As an addendum, performance over the in-sample 2008 financial crisis was reported. The final Objective (7) addressed management and conservation strategies for the NMBM. The NMBM wetland database that was produced during this research is currently being used by the Municipality and will be added to the latest National Wetland Map. From the database, and tools developed in this research, approximately 90 wetlands have been identified as being highly vulnerable due to anthropogenic and environmental factors (Chapter 6) and should be earmarked as key conservation priority areas. Based on field experience and data collected, this study has also made conservation and rehabilitation recommendations for eight locations. Recommendations are also provided for six more wetland systems (or regions) that should be prioritised for further research, as these systems lack fundamental information on where the threat of anthropogenic activities affecting them is greatest. This study has made a significant contribution to understanding the underlying geomorphological processes in depressions, seeps and wetland flats. The desktop mapping component of this study illustrated the dominance of wetlands in the wetter parts of the Municipality. Perched wetland systems were identified in the field, on shallow bedrock, calcrete or clay. The prevalence of these perches in depressions, seeps and wetland flats also highlighted the importance of rainfall in driving wetland formation, by allowing water to pool on these perches, in the NMBM. These perches are likely to be a key factor in the high number of small, ephemeral wetlands that were observed in the study area, compared to other semi-arid regions. Therefore, this research highlights the value of multi-faceted and multi-scalar wetland research and how similar approaches should be used in future research methods has been highlighted. The approach used, along with the tools/methods developed in this study have facilitated the establishment of priority areas for conservation and management within the NMBM. Furthermore, the research approach has revealed emergent wetland properties that are only apparent when looking at different spatial scales. This research has highlighted the complex biological and geomorphological interactions between wetlands that operate over various spatial and temporal scales. As such, wetland management should occur across a wetland complex, rather than individual sites, to account for these multi-scalar influences

Extreme Dependence in Asset Markets Around the Globe

The dependence between large stock returns is higher than the dependence between small to moderate stock returns. This is defined as extreme dependence, and it is particularly observed for large negative returns. Therefore, diversification gains calculated from the overall dependence will overestimate the true potential for diversification during turmoil periods. This thesis answers questions on how the dependence between large negative stock returns can appropriately be modelled. The main conclusions of this thesis read that extreme dependence is often present, can become rather strong, should not be ignored, and shows substantial time-variation. More specifically, extreme dependence shows up as contagion, with small local crashes evolving into more severe crashes. In addition, due to financial globalization, and emerging market liberalization in particular, extreme dependence between regional stock markets has substantially increased. Furthermore, extreme dependence can vary over time by becoming weaker or stronger, but it can also be subject to structural changes, such as a change from symmetric dependence to asymmetric dependence. Using return data at the highest possible level of detail, improves the accuracy of forecasting joint extreme negative returns. Finally, this thesis shows how different econometric techniques can be used for modelling extreme dependence. The use of copulas for financial data is relatively new, therefore a substantial part of this thesis is devoted to new copula models and applications. Other techniques used in this thesis are GARCH, regime-switching, and logit models

Copula-based statistical modelling of synoptic-scale climate indices for quantifying and managing agricultural risks in australia

Australia is an agricultural nation characterised by one of the most naturally diverse climates in the world, which translates into significant sources of risk for agricultural production and subsequent farm revenues. Extreme climatic events have been significantly affecting large parts of Australia in recent decades, contributing to an increase in the vulnerability of crops, and leading to subsequent higher risk to a large number of agricultural producers. However, attempts at better managing climate related risks in the agricultural sector have confronted many challenges. First, crop insurance products, including classical claim-based and index-based insurance, are among the financial implements that allow exposed individuals to pool resources to spread their risk. The classical claim-based insurance indemnifies according to a claim of crop loss from the insured customer, and so can easily manage idiosyncratic risk, which is the case where the loss occurs independently.Nevertheless, the existence of systemic weather risk (covariate risk), which is the spread of extreme events over locations and times (e.g., droughts and floods), has been identified as the main reason for the failure of private insurance markets, such as the classical multi-peril crop insurance, for agricultural crops. The index-based insurance is appropriate to handle systemic but not idiosyncratic risk. The indemnity payments of the index-based insurance are triggered by a predefined threshold of an index (e.g., rainfall), which is related to such losses. Since the covariate nature of a climatic event, it sanctions the insurers to predict losses and ascertain indemnifications for a huge number of insured customers across a wide geographical area. However, basis risk, which is related to the strength of the relationship between the predefined indices used to estimate the average loss by the insured community and the actual loss of insured assets by an individual, is a major barrier that hinders uptake of the index-based insurance. Clearly, the high basis risk, which is a weak relationship between the index and loss, destroys the willingness of potential customers to purchase this insurance product. Second, the impact of multiple synoptic-scale climate mode indices (e.g., Southern Oscillation Index (SOI) and Indian Ocean Index (IOD)) on precipitation and crop yield is not identical in different spatial locations and at different times or seasons across the Australian continent since the influence of large-scale climate heterogeneous over the different regions. The occurrence, role, and amplitude of synoptic-scale climate modes contributing to the variability of seasonal crop production have shifted in recent decades. These variables generally complicate the climate and crop yield relationship that cannot be captured by traditional modelling and analysis approaches commonly found in published agronomic literature such as linear regression. In addition, the traditional linear analysis is not able to model the nonlinear and asymmetric interdependence between extreme insurance losses, which may occur in the case of systemic risk. Relying on the linear method may lead to the problem that different behaviour may be observed from joint distributions, particularly in the upper and lower regions, with the same correlation coefficient. As a result, the likelihood of extreme insurance losses can be underestimated or overestimated that lead to inaccuracies in the pricing of insurance policies. Another alternative is the use of the multivariate normal distribution, where the joint distribution is uniquely defined using the marginal distributions of variables and their correlation matrix. However, phenomena are not always normally distributed in practice. It is therefore important to develop new, scientifically verified, strategic measures to solve the challenges as mentioned above in order to support mitigating the influences of the climate-related risk in the agricultural sector. Copulas provide an advanced statistical approach to model the joint distribution of multivariate random variables. This technique allows estimating the marginal distributions of individual variables independently with their dependence structures. It is clear that the copula method is superior to the conventional linear regression since it does not require variables have to be normally distributed and their correlation can be either linear or non-linear. This doctoral thesis therefore adopts the advanced copula technique within a statistical modelling framework that aims to model: (1) The compound influence of synoptic-scale climate indices (i.e., SOI and IOD) and climate variables (i.e., precipitation) to develop a probabilistic precipitation forecasting system where the integrated role of different factors that govern precipitation dynamics are considered; (2) The compound influence of synoptic-scale climate indices on wheat yield; (3) The scholastic interdependencies of systemic weather risks where potential adaptation strategies are evaluated accordingly; and (4) The risk-reduction efficiencies of geographical diversifications in wheat farming portfolio optimisation. The study areas are Australia’s agro-ecological (i.e., wheat belt) zones where major seasonal wheat and other cereal crops are grown. The results from the first and second objectives can be used for not only forecasting purposes but also understanding the basis risk in the case of pricing climate index-based insurance products. The third and fourth objectives assess the interactions of drought events across different locations and in different seasons and feasible adaptation tools. The findings of these studies can provide useful information for decision-makers in the agricultural sector. The first study found the significant relationship between SOI, IOD, and precipitation. The results suggest that spring precipitation in Australia, except for the western part, can be probabilistically forecasted three months ahead. It is more interesting that the combination of SOI and IOD as the predictors will improve the performance of the forecast model. Similarly, the second study indicated that the largescale climate indices could provide knowledge of wheat crops up to six months in advance. However, it is noted that the influence of different climate indices varies over locations and times. Furthermore, the findings derived from the third study demonstrated the spatio-temporally stochastic dependence of the drought events. The results also prove that time diversification is potentially more effective in reducing the systemic weather risk compared to spatially diversifying strategy. Finally, the fourth objective revealed that wheat-farming portfolio could be effectively optimised through the geographical diversification. The outcomes of this study will lead to the new application of advanced statistical tools that provide a better understanding of the compound influence of synoptic-scale climatic conditions on seasonal precipitation, and therefore on wheat crops in key regions over the Australian continent. Furthermore, a comprehensive analysis of systemic weather risks performed through advanced copula-statistical models can help improve and develop novel agricultural adaptation strategies in not only the selected study region but also globally, where climate extreme events pose a serious threat to the sustainability and survival of the agricultural industry. Finally, the evaluation of the effectiveness of diversification strategies implemented in this study reveals new evidence on whether the risk pooling methods could potentially mitigate climate risks for the agricultural sector and subsequently, help farmers in prior preparation for uncertain climatic events

The GARCH-EVT-Copula model and simulation in scenario-based asset allocation

Financial market integration, in particular, portfolio allocations from advanced economies to South African markets, continues to strengthen volatility linkages and quicken volatility transmissions between participating markets. Largely as a result, South African portfolios are net recipients of returns and volatility shocks emanating from major world markets. In light of these, and other, sources of risk, this dissertation proposes a methodology to improve risk management systems in funds by building a contemporary asset allocation framework that offers practitioners an opportunity to explicitly model combinations of hypothesised global risks and the effects on their investments. The framework models portfolio return variables and their key risk driver variables separately and then joins them to model their combined dependence structure. The separate modelling of univariate and multivariate (MV) components admits the benefit of capturing the data generating processes with improved accuracy. Univariate variables were modelled using ARMA-GARCH-family structures paired with a variety of skewed and leptokurtic conditional distributions. Model residuals were fit using the Peaks-over-Threshold method from Extreme Value Theory for the tails and a non-parametric, kernel density for the interior, forming a completed semi-parametric distribution (SPD) for each variable. Asset and risk factor returns were then combined and their dependence structure jointly modelled with a MV Student t copula. Finally, the SPD margins and Student t copula were used to construct a MV meta t distribution. Monte Carlo simulations were generated from the fitted MV meta t distribution on which an out-of-sample test was conducted. The 2014-to-2015 horizon served to proxy as an out-of-sample, forward-looking scenario for a set of key risk factors against which a hypothetical, diversified portfolio was optimised. Traditional mean-variance and contemporary mean-CVaR optimisation techniques were used and their results compared. As an addendum, performance over the in-sample 2008 financial crisis was reported. The final Objective (7) addressed management and conservation strategies for the NMBM. The NMBM wetland database that was produced during this research is currently being used by the Municipality and will be added to the latest National Wetland Map. From the database, and tools developed in this research, approximately 90 wetlands have been identified as being highly vulnerable due to anthropogenic and environmental factors (Chapter 6) and should be earmarked as key conservation priority areas. Based on field experience and data collected, this study has also made conservation and rehabilitation recommendations for eight locations. Recommendations are also provided for six more wetland systems (or regions) that should be prioritised for further research, as these systems lack fundamental information on where the threat of anthropogenic activities affecting them is greatest. This study has made a significant contribution to understanding the underlying geomorphological processes in depressions, seeps and wetland flats. The desktop mapping component of this study illustrated the dominance of wetlands in the wetter parts of the Municipality. Perched wetland systems were identified in the field, on shallow bedrock, calcrete or clay. The prevalence of these perches in depressions, seeps and wetland flats also highlighted the importance of rainfall in driving wetland formation, by allowing water to pool on these perches, in the NMBM. These perches are likely to be a key factor in the high number of small, ephemeral wetlands that were observed in the study area, compared to other semi-arid regions. Therefore, this research highlights the value of multi-faceted and multi-scalar wetland research and how similar approaches should be used in future research methods has been highlighted. The approach used, along with the tools/methods developed in this study have facilitated the establishment of priority areas for conservation and management within the NMBM. Furthermore, the research approach has revealed emergent wetland properties that are only apparent when looking at different spatial scales. This research has highlighted the complex biological and geomorphological interactions between wetlands that operate over various spatial and temporal scales. As such, wetland management should occur across a wetland complex, rather than individual sites, to account for these multi-scalar influences

Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain

The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio