Maria Elena De Giuli

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.

Bayesian Value-at-Risk with product partition models

In this paper we propose a novel Bayesian methodology for Value-at-Risk computation based on parametric Product Partition Models. Value-at-Risk is a standard tool for measuring and controlling the market risk of an asset or portfolio, and is also required for regulatory purposes. Its popularity is partly due to the fact that it is an easily understood measure of risk. The use of Product Partition Models allows us to remain in a Normal setting even in the presence of outlying points, and to obtain a closed-form expression for Value-at-Risk computation. We present and compare two different scenarios: a product partition structure on the vector of means and a product partition structure on the vector of variances. We apply our methodology to an Italian stock market data set from Mib30. The numerical results clearly show that Product Partition Models can be successfully exploited in order to quantify market risk exposure. The obtained Value-at-Risk estimates are in full agreement with Maximum Likelihood approaches, but our methodology provides richer information about the clustering structure of the data and the presence of outlying points.

Bayesian outlier detection in Capital Asset Pricing Model

We propose a novel Bayesian optimization procedure for outlier detection in the Capital Asset Pricing Model. We use a parametric product partition model to robustly estimate the systematic risk of an asset. We assume that the returns follow independent normal distributions and we impose a partition structure on the parameters of interest. The partition structure imposed on the parameters induces a corresponding clustering of the returns. We identify via an optimization procedure the partition that best separates standard observations from the atypical ones. The methodology is illustrated with reference to a real dataset, for which we also provide a microeconomic interpretation of the detected outliers.

Pure Capital Rationing Problems: How to Bury Them and Why

A usual version of pure capital rationing problems with consistent optima is recalled in Sec. 1. Sec. 2 criticizes some known results and clarifies the assumptions hidden there; their proofs are made quicker in Sec. 4. By means of a very general theorem of the alternative for linear systems (see Sec. 7), three theorems in Sec. 3 put forward necessary and sufficient conditions for the existence of consistent optima, according to the various assumptions on the discounting factors. Sec. 5 points out that such an optimum leads to a vicious circle in fixing the budgets and looks like a machine which doubles their financial value. Sec. 6 shows that these worrying results come from an improper fitting of a well-known application of linear programming in activity analysis. These conclusions claim for non-pure capital rationing problems, i.e. with borrowing and lending opportunities.

Multivariate dependence analysis via tree copula models: An application to one-year forward energy contracts

Abstract We propose a novel multivariate approach for dependence analysis in the energy market. The methodology is based on tree copulas and GARCH type processes. We use it to study the dependence structure among the main factors affecting energy price, and to perform portfolio risk evaluation. The temporal dynamic of the examined variables is described via a set of GARCH type models where the joint distribution of the standardised residuals is represented via suitable tree copula structures. Working in a Bayesian framework, we perform both qualitative and quantitative learning. Posterior summaries of the quantities of interest are obtained via MCMC methods.

Small Sample Properties of Copula-GARCH Modelling: A Monte Carlo Study

Copula-GARCH models have been recently proposed in the financial literature as a statistical tool to deal with flexible multivariate distributions. Our extensive simulation studies investigate the small sample properties of these models and examine how misspecification in the marginals may affect the estimation of the dependence function represented by the copula. We show that the use of Normal marginals when the true Data Generating Process (DGP) is leptokurtic or asymmetric, produces negatively biased estimates of the Normal copula correlations. A striking result is that these biases reach their highest value when correlations are strongly negative, and viceversa. This result remains unchanged with both positively skewed and negatively skewed data, while no biases are found if the variables are uncorrelated. Besides, the effect of marginals asymmetry on correlations is smaller than that of leptokurtosis. We finally analyse the performance of these models in terms of numerical convergence and positive definiteness of the estimated copula correlation matrix.

Non-Substitution Theorems for Perfect Matching Problems

This paper recovers and improves, in a systematic way and under less strict assumptions than the classical ones, some known results pertaining to perfect matching problems. It also puts forward a rule for choosing the vectors of future cash-drawings which lead to a common term structure of interest rates. These results are then framed into the theory of non-substitution theorems for linear economic models. In this area a special perfect matching problem dealing with strict investment projects is analyzed.

Project analysis using a linear approach (P.A.U.L.A.)

We define a general model (called PAULA) for the valuation, optimal management and selection among mutually exclusive safe projects. By exploiting the formal and financial features of the associated linear problems (primal and dual), we put forward two proposals to define an optimal internal financial law (IFL). They may be used to reduce the multiplicity of the IFLs and to avoid economically arbitrary outcomes.RiassuntoSi definisce un modello generale (PAULA) per la valutazione, selezione e gestione ottimale di progetti certi alternativi. Sfruttando i risvolti formali e finanziari dei problemi lineari associati (diretto e duale), si formulano poi due proposte per definire una legge finanziaria interna (IFL) ottimale, utili sia per abbattere la molteplicità intrinseca delleIFL, sia per evitare risultati economicamente arbitrari nel loro uso.

An Integrated Approach to Explore the Complexity of Interest Rates Network Structure

We represent the relationships among interest rates of the same term structure using an integrated approach, which combines quantile regression and graphs. First, the correlation matrix estimated via the quantile regression (QR) is used to explore the inner links among interest rates with different maturity. This lets us possible to check for quantile cointegration among short and long-term interest rates and to assess the Expectations Hypothesis of the term structure. Second, we use these inner links to build the Minimum Spanning Tree (MST) and we investigate the topological role of maturities as centres of a network, in an application focusing on the European interest rates term structure in the period 2006–2017. To validate our choice, we compare the MST built upon the quantile regression to the one based on the sample correlation matrix. The results highlight that the QR exalts the prominent role of short-term interest rates; moreover, the connections among interest rates of the same term structure seem being better captured and described by our procedure rather than by the methodology relying on the estimation of the sample correlation matrix.

Bayesian Networks for Financial Market Signals Detection

In order to model and explain the dynamics of the market, different types and sources of information should be taken into account. We propose to use a Bayesian network as a quantitative financial tool for market signals detection. We combine and incorporate in the model, accounting, market, and sentiment data. The network is used to describe the relationships among the examined variables in an immediate way. Furthermore, it permits to identify in a mouse-click time scenario that could lead to operative signals. An application to the analysis of S&P 500 index is presented.