Luciana Dalla Valle

Copulae and Operational Risks

The management of Operational Risks has always been difficult due to the high number of variables to work with and their complex multivariate distribution. A Copula is a statistic tool which has been recently used in finance and engineering to build flexible joint distributions in order to model a high number of variables. The goal of this paper is to propose its use to model Operational Risks, by showing its benefits with an empirical example.

Bayesian Copulae Distributions, with Application to Operational Risk Management

The aim of this paper is to introduce a new methodology for operational risk management, based on Bayesian copulae. One of the main problems related to operational risk management is understanding the complex dependence structure of the associated variables. In order to model this structure in a flexible way, we construct a method based on copulae. This allows us to split the joint multivariate probability distribution of a random vector of losses into individual components characterized by univariate marginals. Thus, copula functions embody all the information about the correlation between variables and provide a useful technique for modelling the dependency of a high number of marginals. Another important problem in operational risk modelling is the lack of loss data. This suggests the use of Bayesian models, computed via simulation methods and, in particular, Markov chain Monte Carlo. We propose a new methodology for modelling operational risk and for estimating the required capital. This methodology combines the use of copulae and Bayesian models.

Default Probability Estimation via Pair Copula Constructions

In this paper we present a novel approach for firm default probability estimation. The methodology is based on multivariate contingent claim analysis and pair copula constructions. For each considered firm, balance sheet data are used to assess the asset value, and to compute its default probability. The asset pricing function is expressed via a pair copula construction, and it is approximated via Monte Carlo simulations. The methodology is illustrated through an application to the analysis of both operative and defaulted firms.

Official Statistics Data Integration Using Copulas

Abstract The aim of this paper is to propose a novel approach to integrate financial information, incorporating the dependence structure among the variables in the model. The approach is based on two types of graphical models: vines and non-parametric Bayesian belief nets (NPBBNs). Vines are undirected graphs, representing pair copula constructions, which are used to model the dependence structure of a set of variables. NPBBNs are directed graphs, that use pair copulas to model the dependencies, and allow US for diagnosis and prediction via conditionalization. This approach permits to aggregate information and to calibrate the results obtained with different sources of data. The illustrated methodologies are applied to two financial datasets, the first one containing data collected through a survey and the second one containing official statistics data.

Bayesian Model Selection for Beta Autoregressive Processes

We deal with Bayesian inference for Beta autoregressive processes. We restrict our attention to the class of conditionally linear processes. These processes are particularly suitable for forecasting purposes, but are difficult to estimate due to the constraints on the parameter space. We provide a full Bayesian approach to the estimation and include the parameter restrictions in the inference problem by a suitable specification of the prior distributions. Moreover in a Bayesian framework parameter estimation and model choice can be solved simultaneously. In particular we suggest a Markov-Chain Monte Carlo (MCMC) procedure based on a Metropolis-Hastings within Gibbs algorithm and solve the model selection problem following a reversible jump MCMC approach.

Official Statistics Data Integration for Enhanced Information Quality

This work is about integrated analysis of data collected as official statistics with administrative data from operational systems in order to increase the quality of information. Information quality, or InfoQ, is ‘the potential of a data set to achieve a specific goal by using a given empirical analysis method’. InfoQ is based on the identification of four interacting components: the analysis goal, the data, the data analysis and the utility, and it is assessed through eight dimensions: data resolution, data structure, data integration, temporal relevance, generalizability, chronology of data and goal, construct operationalization and communication. The paper illustrates, through case studies, a novel strategy to increase InfoQ based on the integration of official statistics with administrative data using copulas and Bayesian Networks. Official statistics are extraordinary sources of information. However, because of temporal relevance and chronology of data and goals, these fundamental sources of information are often not properly leveraged resulting in a poor level of InfoQ in the use of official statistics. This leads to low valued statistical analyses and to the lack of sufficiently informative results. By improving temporal relevance and chronology of data and goals, the use of Bayesian Networks allows us to calibrate official with administrative data, thus strengthening the quality of the information derived from official surveys, and, overall, enhancing InfoQ. We show, with examples, how to design and implement such a calibration strategy. Copyright

Internationalisation, cultural distance and country characteristics: a Bayesian analysis of SMEs financial performance

Relying on the accounting data of a panel of 403 Italian manufacturing SMEs collected over a period of 5 years, we find results suggesting that multinationality per se does not impact on the economic performance of international small and medium sized firms. It is the characteristics of the country selected, i.e. the political hazard, the financial stability and the economic performance, that significantly influence SMEs financial performance. The management implication for small and medium sized firms selecting and entering new geographic markets is significant, since our results show that for SMEs it is the market selection process that really matters and not the degree of multinationality.

A New Multinomial Model and a Zero Variance Estimation

The analysis of categorical response data through the multinomial model is very frequent in many statistical, econometric, and biometric applications. However, one of the main problems is the precise estimation of the model parameters when the number of observations is very low. We propose a new Bayesian estimation approach where the prior distribution is constructed through the transformation of the multivariate beta of Olkin and Liu (2003). Moreover, the application of the zero-variance principle allows us to estimate moments in Monte Carlo simulations with a dramatic reduction of their variances. We show the advantages of our approach through applications to some toy examples, where we get efficient parameter estimates.

Social Media Big Data Integration: a New Approach Based on Calibration

Abstract In recent years, the growing availability of huge amounts of information, generated in every sector at high speed and in a wide variety of forms and formats, is unprecedented. The ability to harness big data is an opportunity to obtain more accurate analyses and to improve decision-making in industry, government and many other organizations. However, handling big data may be challenging and proper data integration is a key dimension in achieving high information quality. In this paper, we propose a novel approach to data integration that calibrates online generated big data with interview based customer survey data. A common issue of customer surveys is that responses are often overly positive, making it difficult to identify areas of weaknesses in organizations. On the other hand, online reviews are often overly negative, hampering an accurate evaluation of areas of excellence. The proposed methodology calibrates the levels of unbalanced responses in different data sources via resampling and performs data integration using Bayesian Networks to propagate the new re-balanced information. In this paper we show, with a case study example, how the novel data integration approach allows businesses and organizations to get a bias corrected appraisal of the level of satisfaction of their customers. The application is based on the integration of online data of review blogs and customer satisfaction surveys from the San Francisco airport. We illustrate how this integration enhances the information quality of the data analytic work in four of InfoQ dimensions, namely, Data Structure, Data Integration, Temporal Relevance and Chronology of Data and Goal.

The Use of Official Statistics in Self-Selection Bias Modeling

Abstract Official statistics are a fundamental source of publicly available information that periodically provides a great amount of data on all major areas of citizens’ lives, such as economics, social development, education, and the environment. However, these extraordinary sources of information are often neglected, especially by business and industrial statisticians. In particular, data collected from small businesses, like small and medium-sized enterprizes (SMEs), are rarely integrated with official statistics data. In official statistics data integration, the quality of data is essential to guarantee reliable results. Considering the analysis of surveys on SMEs, one of the most common issues related to data quality is the high proportion of nonresponses that leads to self-selection bias. This work illustrates a flexible methodology to deal with self-selection bias, based on the generalization of Heckman’s two-step method with the introduction of copulas. This approach allows us to assume different distributions for the marginals and to express various dependence structures. The methodology is illustrated through a real data application, where the parameters are estimated according to the Bayesian approach and official statistics data are incorporated into the model via informative priors.