Modeling Dependencies in Finance using Copulae

In this paper we provide a review of copula theory with applications to finance. We illustrate the idea on the bivariate framework and discuss the simple, elliptical and Archimedean classes of copulae. Since the cop- ulae model the dependency structure between random variables, next we explain the link between the copulae and common dependency measures, such as Kendall's tau and Spearman's rho. In the next section the copulae are generalized to the multivariate case. In this general setup we discuss and provide an intensive literature review of estimation and simulation techniques. Separate section is devoted to the goodness-of-fit tests. The importance of copulae in finance we illustrate on the example of asset allocation problems, Value-at-Risk and time series models. The paper is complemented with an extensive simulation study and an application to financial data.Distribution functions, Dimension Reduction, Risk management, Statistical models

Probabilistic modeling of flood characterizations with parametric and minimum information pair-copula model

This paper highlights the usefulness of the minimum information and parametric pair-copula construction (PCC) to model the joint distribution of flood event properties. Both of these models outperform other standard multivariate copula in modeling multivariate flood data that exhibiting complex patterns of dependence, particularly in the tails. In particular, the minimum information pair-copula model shows greater flexibility and produces better approximation of the joint probability density and corresponding measures have capability for effective hazard assessments. The study demonstrates that any multivariate density can be approximated to any degree of desired precision using minimum information pair-copula model and can be practically used for probabilistic flood hazard assessment

Optimal enterprise risk management and decision making with shared and dependent risks

Includes bibliographical references (pages 27-29).Published as: Journal of Risk and Insurance, vol. 84, no. 4, December 2017, pp. 1127–1169. https://doi.org/10.1111/jori.12140.Dynamic enterprise risk management (ERM) entails holistic decision-making for critical corporate functions such as capital budgeting and risk management. The interplay across business divisions, however, is complicated due to their natural interactions through the shared and dependent risk exposures within an intricate corporate structure. This paper develops an integrated optimization framework via a copula-based decision tree interface to facilitate ERM decision making to meet the specified enterprise goal in a multi-period setting. We illustrate our model and provide managerial insights with a case study for a financial services company engaged in both banking and insurance businesses

A review on probabilistic graphical models in evolutionary computation

Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Evolutionary algorithms is one such discipline that has employed probabilistic graphical models to improve the search for optimal solutions in complex problems. This paper shows how probabilistic graphical models have been used in evolutionary algorithms to improve their performance in solving complex problems. Specifically, we give a survey of probabilistic model building-based evolutionary algorithms, called estimation of distribution algorithms, and compare different methods for probabilistic modeling in these algorithms

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

Vine Copula Approach to Understand the Financial Dependence of the Istanbul Stock Exchange Index

Recently, the complex dependence patterns among various stocks gained more importance. Measuring the dependency structure is critical for investors to manage their portfolio risks. Since the global financial crisis, researchers have been more interested in studying the dynamics of dependency within stock markets by using novel methodologies. This study aims to investigate a Regular-Vine copula approach to estimate the interdependence structure of the Istanbul Stock Exchange index (ISE100). For this purpose, we consider 32 stocks related to 6 sectors belonging to ISE100. To reflect the time-varying impacts of the 2008–2009 global financial crisis, the dependence analysis is conducted over pre-, during-, and post-global financial crisis periods. Portfolio analysis is considered via a rolling window approach to capture the changes in the dependence. We compare the Regular-Vine-based generalized autoregressive conditional heteroskedasticity (GARCH) against the conventional GARCH model with different innovations. Value at risk and expected shortfall risk measures are used to validate the models. Additionally, for the constructed portfolios, return performance is summarized using both Sharpe and Sortino ratios. To test the ability of the considered Regular-Vine approach on ISE100, another evaluation has been done during the COVID-19 pandemic crisis with various parameter settings. The main findings across different risky periods illustrate the suitability of using the Regular-vine GARCH approach to model the complex dependence among stocks in emerging market conditions

Approximate uncertainty modeling in risk analysis with vine copulas

Many applications of risk analysis require us to jointly model multiple uncertain quantities. Bayesian networks and copulas are two common approaches to modelling joint uncertainties with probability distributions. This paper focuses on new methodologies for copulas by developing work of Cooke, Bedford, Kurowica and others on vines as a way of constructing higher dimensional distributions which do not suffer from some of the restrictions of alternatives such as the multivariate Gaussian copula. The paper provides a fundamental approximation result, demonstrating that we can approximate any density as closely as we like using vines. It further operationalizes this result by showing how minimum information copulas can be used to provide parametric classes of copulas which have such good levels of approximation. We extend previous approaches using vines by considering non-constant conditional dependencies which are particularly relevant in financial risk modelling. We discuss how such models may be quantified, in terms of expert judgement or by fitting data, and illustrate the approach by modelling two financial datasets

BOtied: Multi-objective Bayesian optimization with tied multivariate ranks

Many scientific and industrial applications require joint optimization of multiple, potentially competing objectives. Multi-objective Bayesian optimization (MOBO) is a sample-efficient framework for identifying Pareto-optimal solutions. We show a natural connection between non-dominated solutions and the highest multivariate rank, which coincides with the outermost level line of the joint cumulative distribution function (CDF). We propose the CDF indicator, a Pareto-compliant metric for evaluating the quality of approximate Pareto sets that complements the popular hypervolume indicator. At the heart of MOBO is the acquisition function, which determines the next candidate to evaluate by navigating the best compromises among the objectives. Multi-objective acquisition functions that rely on box decomposition of the objective space, such as the expected hypervolume improvement (EHVI) and entropy search, scale poorly to a large number of objectives. We propose an acquisition function, called BOtied, based on the CDF indicator. BOtied can be implemented efficiently with copulas, a statistical tool for modeling complex, high-dimensional distributions. We benchmark BOtied against common acquisition functions, including EHVI and random scalarization (ParEGO), in a series of synthetic and real-data experiments. BOtied performs on par with the baselines across datasets and metrics while being computationally efficient.Comment: 10 pages (+5 appendix), 9 figures. Submitted to NeurIP

Sustainability and firm performance : evidence from corportate and farm level

This thesis approaches the question of sustainability and firm performance. In the contemporary business model, firm performance measurement must take into account not only economic profits, but also environmental and social issues, in order to ensure the sustainable development of the firm. By using advanced methodological approaches and exploring sustainability through a holistic view, this thesis contributes significantly to sustainability performance literature. Three specific objectives have been fulfilled through three papers that constitute the main body of the present thesis. The first article aims to answer whether profitable business is compatible with balanced sustainability by investigating the relationship between the economic, social, environmental and governance performance for a sample of global firms. A canonical vine (C-vine) copula is used for this purpose. Results show the existence of a fairly strong positive relationship between economic, social and environmental performance. The corporate governance dimension is shown to have a weak relationship with the rest of the corporate social responsibility (CSR) dimensions. Important policy implications are derived from these results. The second paper investigates the relationships among performance dimensions associated with corporate social responsibility focusing on the U.S. electric utility sector. Results of a statistical copula approach suggest that economic performance of utilities is compatible with environmental, social, and governance performance. The CSR model has the potential to help U.S. electric utilities become better corporate citizens while also obtaining higher economic profits. The third paper investigates farms’ stochastic production technology as the interaction of three-main types of sub-technologies that govern, respectively, the production of agricultural commodities, environmental pollution, and social outputs of agricultural activities. The model is empirically implemented through a Data Envelopment Analysis (DEA) model. The empirical application is based on a survey of Catalan arable crop farms. On average, we find our sample farms to display high technical and social performance, while they show relatively poor environmental performance.Esta tesis aborda la cuestión de la sostenibilidad y el rendimiento de la empresa. En el modelo de negocio contemporáneo, la medición del rendimiento de la empresa debe tener en cuenta no solo las ganancias económicas, sino también las cuestiones ambientales y sociales, para garantizar el desarrollo sostenible de la empresa. Mediante el uso de enfoques metodológicos avanzados y la exploración de la sostenibilidad a través de una visión holística, esta tesis contribuye significativamente a la literatura sobre la sostenibilidad. Tres objetivos específicos se han cumplido a través de tres documentos que constituyen el cuerpo principal de la presente tesis. El primer artículo tiene como objetivo responder si el negocio rentable es compatible con la sostenibilidad equilibrada, mediante la investigación de la relación entre el desempeño económico, social, medio-ambiental y de gobernanza de una muestra de empresas globales. Un modelo canónico de viña de copulas (C-vine) se usa para este propósito. Los resultados muestran la existencia de una relación positiva bastante fuerte entre el desempeño económico, social y ambiental. Se muestra que la dimensión de gobernanza corporativa tiene una relación débil con el resto de las dimensiones de la responsabilidad social corporativa (RSC). Importantes implicaciones de política se derivan de estos resultados. El segundo articulo investiga las relaciones entre las dimensiones de desempeño asociadas con la responsabilidad social corporativa que se centran en el sector de servicios eléctricos de los EE. UU. Los resultados obtenidos del análisis de las cópulas sugieren que el desempeño económico de las empresas eléctricas es compatible con el desempeño ambiental, social y de gobernanza. El modelo de la RSC tiene el potencial de ayudar a que los servicios eléctricos de los EE. UU. Se conviertan en mejores ciudadanos corporativos mientras se logran mayores beneficios económicos. El tercer trabajo investiga la tecnología de producción estocástica de las explotaciones agrícolas como una interacción de tres sub-tecnologías que gobiernan, respectivamente, la producción de productos agrícolas, la contaminación ambiental y los productos sociales de las actividades agrícolas. El modelo se implementa empíricamente a través de un modelo de Análisis Envolvente de Datos (DEA). La aplicación empírica se basa en una encuesta de explotaciones de cultivos en la región de Cataluña. En promedio, encontramos que nuestras explotaciones muestran un alto desempeño técnico y social, mientras que muestran un desempeño ambiental relativamente pobre