Risks

This book is a collection of feature articles published in Risks in 2020. They were all written by experts in their respective fields. In these articles, they all develop and present new aspects and insights that can help us to understand and cope with the different and ever-changing aspects of risks. In some of the feature articles the probabilistic risk modeling is the central focus, whereas impact and innovation, in the context of financial economics and actuarial science, is somewhat retained and left for future research. In other articles it is the other way around. Ideas and perceptions in financial markets are the driving force of the research but they do not necessarily rely on innovation in the underlying risk models. Together, they are state-of-the-art, expert-led, up-to-date contributions, demonstrating what Risks is and what Risks has to offer: articles that focus on the central aspects of insurance and financial risk management, that detail progress and paths of further development in understanding and dealing with...risks. Asking the same type of questions (which risk allocation and mitigation should be provided, and why?) creates value from three different perspectives: the normative perspective of market regulator; the existential perspective of the financial institution; the phenomenological perspective of the individual consumer or policy holder

A Lévy Option Pricing model of FFT-Based High-order Multinomial Tree

This paper studies the method of constructing high order recombined multinomial tree based on fast Fourier transform (FFT), and applies multinomial tree option pricing under the Lévy process. First, the Lévy option pricing model and Fourier transform are introduced. Then, the network model based on FFT (Markov chain) is presented. After that, a method of constructing a recombined multinomial tree based on FFT is given. It is proved that the discrete random variables corresponding to the multinomial tree converge to the Lévy distributed continuous random variable. Next, we obtain the European option pricing formula of FFT multinomial tree pricing, and apply the reverse iteration method to the American option pricing. Finally, under the Jump-diffuse process, the difference between the computational accuracy and computational efficiency of the Semi-analytical solution of European Option and Merton European Call Option which are priced under FFT is compared. The results show that the method of constructing a high-order recombined multinomial tree based on FFT has very high calculation precision and calculation speed, which can solve the problem of traditional risk-neutral multinomial tree construction and it is a promising pricing method for derivative products

Innovations in Quantitative Risk Management

Quantitative Finance; Game Theory, Economics, Social and Behav. Sciences; Finance/Investment/Banking; Actuarial Science

Innovations in Quantitative Risk Management

Quantitative Finance; Game Theory, Economics, Social and Behav. Sciences; Finance/Investment/Banking; Actuarial Science

Essays in Financial Markets

This dissertation is a collection of three essays that analyze the impact of economic uncertainty on financial market activities and evaluate alternative quantitative models for economic uncertainty based on financial asset prices. Chapter 1 is motivated by the fact that major economic and political shocks, such as the Cuban missile crisis, the 9/11 terrorist attacks, and the 2008 financial crisis, trigger spikes in market-wide uncertainty. It develops a dynamic trading model to analyze the impacts of these uncertainty shocks on the behaviors of market liquidity and shows how such impacts differ from those caused by shocks to economic conditions. According to my model, an uncertainty shock triggers a temporary decline in market liquidity, because an uncertainty shock introduces ambiguity and learning can resolve this ambiguity. Meanwhile, incorporating the notion of time-varying uncertainty aversion, my model implies that a shock to economic condition generates a persistent decline in market liquidity, since learning does not affect uncertainty aversion. My VAR estimations using monthly US data for 1962--2013 lend support to my model implications. An uncertainty shock generates a rapid drop and rebound in overall stock market liquidity for around five months on average, while a shock to economic condition leads to a persistent decline in market liquidity for up to a year. Chapter 2 examines the ability of five basis alternative option pricing models to price the early exercise premium (EEP) in American put prices: Black-Scholes model, Heston (1993) stochastic volatility model, and three jump pricing models – Merton (1976), Madan et al. (1998), and Carr and Wu (2003). After duly accounting for the market implied value of the Fleming and Whaley (1993) wild card option, we find that jump models perform best in pricing observed EEP. Importantly, all models consistently and significantly underprice observed EEP, where this underpricing is more pronounced for short term in-the-money EEP. We argue and empirically demonstrate that trading costs in the option market generate a significant EEP by incentivizing and rewarding early exercise of American options that would alternatively have been “sold” in the market. Chapter 3 examines the frequency and character of price jumps in front month oil and natural gas futures prices, where prices are sampled every five seconds over the period 2006-2014. We find that an infinite activity jump diffusion process describes crude oil and natural gas futures returns combined with a process involving much larger but less frequent jumps. We further find that jumps account for respectively 36 and 41 percent of the realized variances of the crude oil and the natural gas returns

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

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

Empirical essays in quantitative risk management

Copula theory is particularly useful for modeling multivariate distributions as it allows us to decompose a joint distribution into marginal distributions and a copula. Copula-based models have been widely applied in finance, insurance, macroeconomics, microeconomics and many other areas in recent years. This doctoral thesis particularly pays attention to applications of copula theory in quantitative risk management. The first chapter of this thesis provides a comprehensive review of recent developments of copula models and some important applications in the large and growing finance and economics literature. The first part of this chapter briefly introduces the definition and properties of copulas as well as several related concepts. The second part reviews estimation and inference methods, goodness-of-fit tests and model selection tests for copula models considered in the literature. The third part provides an exhaustive review of the extensive literature of copula-based models in finance and economics. Finally, an interesting topic for further research is suggested. The remaining three chapters investigate applications of copula theory in three topics: market risk prediction, portfolio optimization and credit risk estimation. Chapter Two investigates the dynamic and asymmetric dependence structure between equity portfolios from the US and UK. We demonstrate the statistical significance of dynamic asymmetric copula models in modeling and forecasting market risk. First, we construct ``high-minus-low" equity portfolios sorted on beta, coskewness, and cokurtosis. We find substantial evidence of dynamic and asymmetric dependence between characteristic-sorted portfolios. Second, we consider a dynamic asymmetric copula model by combining the generalized hyperbolic skewed t copula with the generalized autoregressive score (GAS) model to capture both the multivariate non-normality and the dynamic and asymmetric dependence between equity portfolios. We demonstrate the usefulness of this model by evaluating the forecasting performance of Value-at-Risk and Expected Shortfall for high-minus-low portfolios. From backtesting, we find consistent and robust evidence that our dynamic asymmetric copula model provides the most accurate forecasts, indicating the importance of incorporating the dynamic and asymmetric dependence structure in risk management. Chapter Three investigates the dependence between equity and currency in international financial markets and explores its economic importance in portfolio allocation. First, we find striking evidence for the existence of time-varying and asymmetric dependence between equity and currency. Second, we offer a methodological contribution. A novel time-varying skewed t copula (TVAC) model is proposed to accommodate non-Gaussian features in univariate time series as well as the dynamic and asymmetric dependence in multivariate time series. The multivariate asymmetry is captured by the skewed t copula derived from the mutlivariate skewed t distribution in Bauwens and Laurent (2005) and the time-varying dependence is captured by the GAS dynamics proposed by Creal et al. (2013). This model can be easily generalized from the bivariate case to the multivariate case. Third, we show that findings of dynamic and asymmetric dependence between equity and currency have important implications for risk management and asset allocation in international financial markets. Our empirical results show the statistical significance of the TVAC model in risk management and its economic values in real-time investment. Chapter Four studies the credit risk of UK top-tier banks. We document asymmetric and time-varying features of dependence between the credit risk of UK top tier banks using a new CDS dataset. The market-implied probability of default for individual banks is derived from observed market quotes of CDS. The default dependence between banks is modeled by a novel dynamic asymmetric copula framework. We show that all the empirical features of CDS spreads, such as heavy-tailedness, skewness, time-varying volatility, multivariate asymmetries and dynamic dependence, can be captured well by our model. Given the marginal default probability and estimated copula model, we compute the joint and conditional probability of default of UK banks by applying a fast simulation algorithm. Comparing our model with traditional copula models, we find that the traditional models may underestimate the joint credit risk most of the time, especially during a crisis. Furthermore, we perform an extensive regression analysis and find solid evidence that time-varying tail dependence between CDS spreads of UK banks contains useful information to explain and predict their joint and conditional default probabilities. Chapter Five concludes with recommendations for further study