Kjersti Aas

Models for construction of multivariate dependence - a comparison study

A multivariate data set, which exhibit complex patterns of dependence, particularly in the tails, can be modelled using a cascade of lower-dimensional copulae. In this paper, we compare two such models that differ in their representation of the dependency structure, namely the nested Archimedean construction (NAC) and the pair-copula construction (PCC). The NAC is much more restrictive than the PCC in two respects. There are strong limitations on the degree of dependence in each level of the NAC, and all the bivariate copulas in this construction has to be Archimedean. Based on an empirical study with two different four-dimensional data sets; precipitation values and equity returns, we show that the PCC provides a better fit than the NAC and that it is computationally more efficient. Hence, we claim that the PCC is more suitable than the NAC for hich-dimensional modelling.

On the simplified pair-copula construction - Simply useful or too simplistic?

Due to their high flexibility, yet simple structure, pair-copula constructions (PCCs) are becoming increasingly popular for constructing continuous multivariate distributions. However, inference requires the simplifying assumption that all the pair-copulae depend on the conditioning variables merely through the two conditional distribution functions that constitute their arguments, and not directly. In terms of standard measures of dependence, we express conditions under which a specific pair-copula decomposition of a multivariate distribution is of this simplified form. Moreover, we show that the simplified PCC in fact is a rather good approximation, even when the simplifying assumption is far from being fulfilled by the actual model.

Integrated Risk Modelling

In this article, we present a new approach to modelling the total economic capital required to protect a financial institution against possible losses. The approach takes into account the correlation between risk types, and in this respect, it improves upon the conventional practice that assumes perfectly correlated risks. A statistical model is built, and Monte Carlo simulation is used to estimate the total loss distribution. The methodology has been implemented in the Norwegian financial group DnB’s system for risk management. Incorporating current expert knowledge of relationships between risks, rather than taking the most conservative stand, gives a 20% reduction in the total economic capital for a one year time horizon.

Applications of hidden Markov chains in image analysis

In image analysis, two-dimensional Markov models, i.e. Markov field models, have been applied for segmentation purposes, but except for the area of text recognition, the application of hidden Markov chains has been rare. Through four very different examples, this paper demonstrates the applicability also for hidden Markov chains in image analysis, and shows that the problems of image analysis often may have one- dimensional characteristics even though the images are two-dimensional.

Risk estimation using the multivariate normal inverse Gaussian distribution

Appropriate modeling of time-varying dependencies is very important for quantifying financial risk, such as the risk associated with a portfolio of financial assets. Most of the papers analyzing financial returns have focused on the univariate case. The few that are concerned with their multivariate extensions are mainly based on the multivariate normal assumption. The idea of this paper is to use the multivariate normal inverse Gaussian (MNIG) distribution as the conditional distribution for a multivariate GARCH model. The MNIG distribution belongs to a very flexible family of distributions that captures heavy tails and skewness in the distribution of individual stock returns, as well as the asymmetry in the dependence between stocks observed in financial time series data. The usefulness of the MNIG GARCH model is highlighted through a value-at-risk (VAR) application on a portfolio of European, American and Japanese equities. Backtesting shows that for a one-day holding period this model outperforms a Gaussian GARCH model and a Students t GARCH model. Moreover, it is slightly better than a skew Students t GARCH model.

Tools for interactive map conversion and vectorization

The process of converting an analog map into structured digitized information requires several different operations, which are all time-consuming when performed manually. Strictly automatic processing is not always a possible solution, and an interactive approach can then be an alternative. The paper describes a tool for map conversion, focusing on the functionality for extraction of line structures. An interactive approach is used as it gives the user an opportunity to survey the process, and utilize human knowledge. The methods are based on contour following, extracting centre points needed for accurate vector representation of the line during tracing.

Text page recognition using Grey-level features and hidden Markov models

This paper presents an approach to text recognition which avoids the problems of thresholding and segmentation by working directly on the grey-level image recognizing an entire word at the time. For each word a sequence of grey-level feature vectors is extracted. Hidden Markov models are used to describe the single characters and the sequence of feature vectors is matched against all possible combinations of models using dynamic programming.

Estimating stochastic volatility models using integrated nested Laplace approximations

Volatility in financial time series is mainly analysed through two classes of models; the generalized autoregressive conditional heteroscedasticity (GARCH) models and the stochastic volatility (SV) ones. GARCH models are straightforward to estimate using maximum-likelihood techniques, while SV models require more complex inferential and computational tools, such as Markov Chain Monte Carlo (MCMC). Hence, although provided with a series of theoretical advantages, SV models are in practice much less popular than GARCH ones. In this paper, we solve the problem of inference for some SV models by applying a new inferential tool, integrated nested Laplace approximations (INLAs). INLA substitutes MCMC simulations with accurate deterministic approximations, making a full Bayesian analysis of many kinds of SV models extremely fast and accurate. Our hope is that the use of INLA will help SV models to become more appealing to the financial industry, where, due to their complexity, they are rarely used in practice.

Modelling and predicting customer churn from an insurance company

Within a companys customer relationship management strategy, finding the customers most likely to leave is a central aspect. We present a dynamic modelling approach for predicting individual customers’ risk of leaving an insurance company. A logistic longitudinal regression model that incorporates time-dynamic explanatory variables and interactions is fitted to the data. As an intermediate step in the modelling procedure, we apply generalised additive models to identify non-linear relationships between the logit and the explanatory variables. Both out-of-sample and out-of-time prediction indicate that the model performs well in terms of identifying customers likely to leave the company each month. Our approach is general and may be applied to other industries as well.

Text Recogniton from Grey Level Images Using Hidden Markovc Models

The problems of character recognition are today mainly due to imperfect thresholding and segmentation. In this paper a new approach to text recognition is presented which attempts to avoid these problems by working directly on grey level images and treating an entire word at the time. The features are found from the grey levels of the image, and a hidden Markov model is defined for each character. During recognition the most probable combination of models is found for each word by the use of dynamic programming.