Modelli matematici applicati alla probabilità di default nei sistemi di rating.

L'obiettivo del seguente lavoro è determinare attraverso l'uso di procedure statistico-econometriche, in particolare del metodo ECM, le previsioni per i tassi di default nel triennio 2013-2015, partendo dalle serie storiche di questi ultimi e da quelle macroeconomiche.

Econometrics of default risk

This thesis is the result of a project aimed at the study of a crucial topic in finance: default risk, whose measurement and modelling have achieved increasing relevance in recent years. We investigate the main issues related to the default phenomenon, under both a methodological and empirical perspective. The topics of default predictability and correlation are treated with a constant attention to the modelling solutions and reviewing critically the literature. From the methodological point of view, our analysis results in the proposal of a new class of models, called Poisson Autoregression with Exogenous Covariates (PARX). The PARX models, including both autoregressive end exogenous components, are able to capture the dynamics of default count time series, characterized by persistence of shocks and slowly decaying autocorrelation. Application of different PARX models to the monthly default counts of US industrial firms in the period 1982-2011 allows an empirical insight of the defaults dynamics and supports the identification of the main default predictors at an aggregate level.

Pricing in stochastic-local volatility models with default

In recent years is becoming increasingly important to handle credit risk. Credit risk is the risk associated with the possibility of bankruptcy. More precisely, if a derivative provides for a payment at cert time T but before that time the counterparty defaults, at maturity the payment cannot be effectively performed, so the owner of the contract loses it entirely or a part of it. It means that the payoff of the derivative, and consequently its price, depends on the underlying of the basic derivative and on the risk of bankruptcy of the counterparty. To value and to hedge credit risk in a consistent way, one needs to develop a quantitative model. We have studied analytical approximation formulas and numerical methods such as Monte Carlo method in order to calculate the price of a bond. We have illustrated how to obtain fast and accurate pricing approximations by expanding the drift and diffusion as a Taylor series and we have compared the second and third order approximation of the Bond and Call price with an accurate Monte Carlo simulation. We have analysed JDCEV model with constant or stochastic interest rate. We have provided numerical examples that illustrate the effectiveness and versatility of our methods. We have used Wolfram Mathematica and Matlab.

Credit-Default-Swaps and the 2008 Financial Crisis: An Inquiry into the Underlying Legal Origins and the European Union’s Regulatory Reforms

After the 2008 financial crisis, the financial innovation product Credit-Default-Swap (CDS) was widely blamed as the main cause of this crisis. CDS is one type of over-the-counter (OTC) traded derivatives. Before the crisis, the trading of CDS was very popular among the financial institutions. But meanwhile, excessive speculative CDSs transactions in a legal environment of scant regulation accumulated huge risks in the financial system. This dissertation is divided into three parts. In Part I, we discussed the primers of the CDSs and its market development, then we analyzed in detail the roles CDSs had played in this crisis based on economic studies. It is advanced that CDSs not just promoted the eruption of the crisis in 2007 but also exacerbated it in 2008. In part II, we asked ourselves what are the legal origins of this crisis in relation with CDSs, as we believe that financial instruments could only function, positive or negative, under certain legal institutional environment. After an in-depth inquiry, we observed that at least three traditional legal doctrines were eroded or circumvented by OTC derivatives. It is argued that the malfunction of these doctrines, on the one hand, facilitated the proliferation of speculative CDSs transactions; on the other hand, eroded the original risk-control legal mechanism. Therefore, the 2008 crisis could escalate rapidly into a global financial tsunami, which was out of control of the regulators. In Part III, we focused on the European Union’s regulatory reform towards the OTC derivatives market. In specific, EU introduced mandatory central counterparty clearing obligation for qualified OTC derivatives, and requires that all OTC derivatives shall be reported to a trade repository. It is observable that EU’s approach in re-regulating the derivatives market is different with the traditional administrative regulation, but aiming at constructing a new market infrastructure for OTC derivatives.

Semantic memory involvement in the default mode network: a functional neuroimaging study using independent component analysis

The Default Mode Network (DMN) is a higher order functional neural network that displays activation during passive rest and deactivation during many types of cognitive tasks. Accordingly, the DMN is viewed to represent the neural correlate of internally-generated self-referential cognition. This hypothesis implies that the DMN requires the involvement of cognitive processes, like declarative memory. The present study thus examines the spatial and functional convergence of the DMN and the semantic memory system. Using an active block-design functional Magnetic Resonance Imaging (fMRI) paradigm and Independent Component Analysis (ICA), we trace the DMN and fMRI signal changes evoked by semantic, phonological and perceptual decision tasks upon visually-presented words. Our findings show less deactivation during semantic compared to the two non-semantic tasks for the entire DMN unit and within left-hemispheric DMN regions, i.e., the dorsal medial prefrontal cortex, the anterior cingulate cortex, the retrosplenial cortex, the angular gyrus, the middle temporal gyrus and the anterior temporal region, as well as the right cerebellum. These results demonstrate that well-known semantic regions are spatially and functionally involved in the DMN. The present study further supports the hypothesis of the DMN as an internal mentation system that involves declarative memory functions.

Reduced Cerebral Blood Flow Within the Default-Mode Network and Within Total Gray Matter in Major Depression

The default-mode network (DMN) was shown to have aberrant blood oxygenation-level-dependent (BOLD) activity in major depressive disorder (MDD). While BOLD is a relative measure of neural activity, cerebral blood flow (CBF) is an absolute measure. Resting-state CBF alterations have been reported in MDD. However, the association of baseline CBF and CBF fluctuations is unclear in MDD. Therefore, the aim was to investigate the CBF within the DMN in MDD, applying a strictly data-driven approach. In 22 MDD patients and 22 matched healthy controls, CBF was acquired using arterial spin labeling (ASL) at rest. A concatenated independent component analysis was performed to identify the DMN within the ASL data. The perfusion of the DMN and its nodes was quantified and compared between groups. The DMN was identified in both groups with high spatial similarity. Absolute CBF values within the DMN were reduced in MDD patients (p<0.001). However, after controlling for whole-brain gray matter CBF and age, the group difference vanished. In patients, depression severity was correlated with reduced perfusion in the DMN in the posterior cingulate cortex and the right inferior parietal lobe. Hypoperfusion within the DMN in MDD is not specific to the DMN. Still, depression severity was linked to DMN node perfusion, supporting a role of the DMN in depression pathobiology. The finding has implications for the interpretation of BOLD functional magnetic resonance imaging data in MDD.

BOLD correlates of EEG alpha phase-locking and the fMRI default mode network

Phase locking or synchronization of brain areas is a key concept of information processing in the brain. Synchronous oscillations have been observed and investigated extensively in EEG during the past decades. EEG oscillations occur over a wide frequency range. In EEG, a prominent type of oscillations is alpha-band activity, present typically when a subject is awake, but at rest with closed eyes. The spectral power of alpha rhythms has recently been investigated in simultaneous EEG/fMRI recordings, establishing a wide-range cortico-thalamic network. However, spectral power and synchronization are different measures and little is known about the correlations between BOLD effects and EEG synchronization. Interestingly, the fMRI BOLD signal also displays synchronous oscillations across different brain regions. These oscillations delineate so-called resting state networks (RSNs) that resemble the correlation patterns of simultaneous EEG/fMRI recordings. However, the nature of these BOLD oscillations and their relations to EEG activity is still poorly understood. One hypothesis is that the subunits constituting a specific RSN may be coordinated by different EEG rhythms. In this study we report on evidence for this hypothesis. The BOLD correlates of global EEG synchronization (GFS) in the alpha frequency band are located in brain areas involved in specific RSNs, e.g. the 'default mode network'. Furthermore, our results confirm the hypothesis that specific RSNs are organized by long-range synchronization at least in the alpha frequency band. Finally, we could localize specific areas where the GFS BOLD correlates and the associated RSN overlap. Thus, we claim that not only the spectral dynamics of EEG are important, but also their spatio-temporal organization.

Investment Valuation with Tax-optimized Financing Decisions and a Tax-optimized Default Alternative

In this paper we evaluate an indivisible investment project that is carried out in a corporation under very simple premises. In particular, we discuss a one-period model with certainty, the pure domestic case and proportional tax rates. Surprisingly, the decision problem turns out to be rather complex if one has to make allowance for different taxation of the corporation and its owner. Altogether there are more than 10 cases that have to be distinguished if the firm's managers want to make a correct decision, depending on the relation of personal and corporate tax rates.

Transcatheter aortic valve implantation: the transfemoral access route is the default access

Transcatheter aortic valve implantation (TAVI) is a widely accepted alternative to surgical aortic valve replacement (SAVR) among non-operable patients or selected high-risk patients with degenerative, severe aortic stenosis. TAVI is considered less invasive when compared with SAVR; however, there remain significant differences between different TAVI access routes. The transfemoral approach is considered the least invasive access route, and can be performed as a fully percutaneous procedure in a spontaneously breathing patient under local anaesthesia and mild sedation only. Moreover, transfemoral TAVI patients are typically transferred to coronary care rather than to an intensive care unit after the procedure, and benefit from early ambulation and a reduction in overall length of hospital stay. Considering these patient-specific and health-economic advantages, several TAVI centres follow the least invasive strategy for their patients and have implemented the transfemoral access route as the default access in their institutions. This article provides an overview on the prerequisites for a successful transfemoral TAVI procedure, describes the procedural advantages compared to alternative access routes, and highlights differences in clinical outcomes.

The brain’s default state interacts with working memory processes in a complex and load-dependent manner

Recently, many studies about a network active during rest and deactivated during tasks emerged in the literature: the default mode network (DMN). Spatial and temporal DMN features are important markers for psychiatric diseases. Another prominent indicator of cognitive functioning, yielding information about the mental condition in health and disease, is working memory (WM) processing. In EEG studies, frontal-midline theta power has been shown to increase with load during WM retention in healthy subjects. From these findings, the conclusion can be drawn that an increase in resting state DMN activity may go along with an increase in theta power in high-load WM conditions. We followed this hypothesis in a study on 17 healthy subjects performing a visual Sternberg WM task. The DMN was obtained by a BOLD-ICA approach and its dynamics represented by the percent-strength during pre-stimulus periods. DMN dynamics were temporally correlated with EEG theta spectral power from retention intervals. This so-called covariance mapping yielded the spatial distribution of the theta EEG fluctuations associated with the dynamics of the DMN. In line with previous findings, theta power was increased at frontal-midline electrodes in high- versus low-load conditions during early WM retention. However, load-dependent correlations of DMN with theta power resulted in primarily positive correlations in low-load conditions, while during high-load conditions negative correlations of DMN activity and theta power were observed at frontal-midline electrodes. This DMN-dependent load effect reached significance during later retention. Our results show a complex and load-dependent interaction of pre-stimulus DMN activity and theta power during retention, varying over the course of the retention period. Since both, WM performance and DMN activity, are markers of mental health, our results could be important for further investigations of psychiatric populations.

The brain’s pre-stimulus default state interacts with working memory in a load-dependent manner

Recently, multiple studies showed that spatial and temporal features of a task-negative default mode network (DMN) (Greicius et al., 2003) are important markers for psychiatric diseases (Balsters et al., 2013). Another prominent indicator of cognitive functioning, yielding information about the mental condition in health and disease, is working memory (WM) processing. In EEG and MEG studies, frontal-midline theta power has been shown to increase with load during WM retention in healthy subjects (Brookes et al., 2011). Negative correlations between DMN activity and theta amplitude have been found during resting state (Jann et al., 2010) as well as during WM (Michels et al., 2010). Likewise, WM training resulted in higher resting state theta power as well as increased small-worldness of the resting brain (Langer et al., 2013). Further, increased fMRI connectivity between nodes of the DMN correlated with better WM performance (Hampson et al., 2006). Hence, the brain’s default state might influence it’s functioning during task. We therefore hypothesized correlations between pre-stimulus DMN activity and EEG-theta power during WM maintenance, depending on the WM load. 17 healthy subjects performed a Sternberg WM task while being measured simultaneously with EEG and fMRI. Data was recorded within a multicenter-study: 12 subjects were measured in Zurich with a 64-channels MR-compatible system (Brain Products) in a 3T Philips scanner, 5 subjects with a 96-channel MR-compatible system (Brain Products) in a 3T Siemens Scanner in Bern. The DMN components was obtained by a group BOLD-ICA approach over the full task duration (figure 1). The subject-wise dynamics were obtained by back-reconstructed onto each subject’s fMRI data and normalized to percent signal change values. The single trial pre-stimulus-DMN activation was then temporally correlated with the single trial EEG-theta (3-8 Hz) spectral power during retention intervals. This so-called covariance mapping (Jann et al., 2010) yielded the spatial distribution of the theta EEG fluctuations during retention associated with the dynamics of the pre-stimulus DMN. In line with previous findings, theta power was increased at frontal-midline electrodes in high- versus low-load conditions during early WM retention (figure 2). However, correlations of DMN with theta power resulted in primarily positive correlations in low-load conditions, while during high-load conditions negative correlations of DMN activity and theta power were observed at frontal-midline electrodes. This DMN-dependent load effect reached significance in the middle of the retention period (TANOVA, p<0.05) (figure 3). Our results show a complex and load-dependent interaction of pre-stimulus DMN activity and theta power during retention, varying over time. While at a more global, load-independent view pre-stimulus DMN activity correlated positively with theta power during retention, the correlation was inversed during certain time windows in high-load trials, meaning that in trials with enhanced pre-stimulus DMN activity theta power decreases during retention. Since both WM performance and DMN activity are markers of mental health our results could be important for further investigations of psychiatric populations.

Prestimulus default mode activity influences depth of processing and recognition in an emotional memory task

Low self-referential thoughts are associated with better concentration, which leads to deeper encoding and increases learning and subsequent retrieval. There is evidence that being engaged in externally rather than internally focused tasks is related to low neural activity in the default mode network (DMN) promoting open mind and the deep elaboration of new information. Thus, reduced DMN activity should lead to enhanced concentration, comprehensive stimulus evaluation including emotional categorization, deeper stimulus processing, and better long-term retention over one whole week. In this fMRI study, we investigated brain activation preceding and during incidental encoding of emotional pictures and on subsequent recognition performance. During fMRI, 24 subjects were exposed to 80 pictures of different emotional valence and subsequently asked to complete an online recognition task one week later. Results indicate that neural activity within the medial temporal lobes during encoding predicts subsequent memory performance. Moreover, a low activity of the default mode network preceding incidental encoding leads to slightly better recognition performance independent of the emotional perception of a picture. The findings indicate that the suppression of internally-oriented thoughts leads to a more comprehensive and thorough evaluation of a stimulus and its emotional valence. Reduced activation of the DMN prior to stimulus onset is associated with deeper encoding and enhanced consolidation and retrieval performance even one week later. Even small prestimulus lapses of attention influence consolidation and subsequent recognition performance. Hum Brain Mapp, 2015. © 2015 Wiley Periodicals, Inc.

Empirical Analysis of Credit Risk Regime Switching and Temporal Conditional Default Correlation in Credit Default Swap Valuation: The Market liquidity effect

In this paper, we extend the debate concerning Credit Default Swap valuation to include time varying correlation and co-variances. Traditional multi-variate techniques treat the correlations between covariates as constant over time; however, this view is not supported by the data. Secondly, since financial data does not follow a normal distribution because of its heavy tails, modeling the data using a Generalized Linear model (GLM) incorporating copulas emerge as a more robust technique over traditional approaches. This paper also includes an empirical analysis of the regime switching dynamics of credit risk in the presence of liquidity by following the general practice of assuming that credit and market risk follow a Markov process. The study was based on Credit Default Swap data obtained from Bloomberg that spanned the period January 1st 2004 to August 08th 2006. The empirical examination of the regime switching tendencies provided quantitative support to the anecdotal view that liquidity decreases as credit quality deteriorates. The analysis also examined the joint probability distribution of the credit risk determinants across credit quality through the use of a copula function which disaggregates the behavior embedded in the marginal gamma distributions, so as to isolate the level of dependence which is captured in the copula function. The results suggest that the time varying joint correlation matrix performed far superior as compared to the constant correlation matrix; the centerpiece of linear regression models.