Basic Insights in Pricing Basket Credit Derivatives

Basket credit derivatives are those financial contracts whose pay–out depends on the credit events ('failure to pay', 'default', etc.) characterizing a portfolio of bonds or loans over a determined time horizon.
We have two main categories of basket credit derivatives. The first is characterized by a pay–out depending on the temporal ranking of the credit events: first–to–default, second–to–default, etc. The second is characterized by a pay–out depending on the percentiles of the portfolio's loss distribution induced by the credit events. The latter is often embedded in securitizations of portfolios of bonds or loans, i.e. CDO.
This paper proposes some basic insights in the pricing of these particularly complex credit derivatives. Whenever possible, we will try to find an analytical approximation to the exact pricing formula, if a closed form solution is not available.
(J.E.L.: G13).     

Multiple patterns in the dynamics of a stock market model

We study a non-linear model of the interactions between stock market prices and the level of assets owned by investment funds. The model dynamics is described, in continuous time, by a smooth vector field in the plane, which presents, under suitable hypotheses, a unique equilibrium point.Our analisis of the system flow is qualitative and focuses on detecting endogenous fluctuations of the state variables, i.e. on checking existence and number of limit cycles.We prove that several, and quite different, dynamical patterns can occur, even in cases where the system isoclines assume that most simple geometrical forms.It is shown, in particular, that the equilibrium point can undergo either a sub-critical or a super-critical Hopf-bifurcation whenever two economically meaningful exogenous parameters are made to cross a given set of critical values. Hence, in the subcritical case, as a trapping region exists, at least two limit cycles appear.Next, we give analytical examples of model-consistent vector fields which present a multiplicity of fluctuating trends, and prove the apparently surprising result that the number of limit cycles can be as large as one wants, provided a specific isocline assumes a cubic shape.Both authors are members of the Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni-G.N.A.F.A. of the Italian Council of Researches-CN.R.The present paper refers to the activities of the National M.U.R.S.T. Group Dinamiche Non Lineari ed Applicazioni alle Scienze Economiche e Sociali.     

Innovation in the Retail Banking Industry: The Diffusion of Credit Scoring

We study technology diffusion in the retail banking industry. Our contribution to the empirical literature is twofold: Firstly, we explore technology diffusion in the financial sector, whose relevance has often been neglected; secondly we focus on credit scoring adoption, a relevant process innovation still under-explored. Estimating a set of duration models, we analyze the patterns of diffusion of this technology among Italian banks. We find that credit scoring is firstly introduced by large banks with broad branch networks, which can fully exploit scale economies. We present robust evidence that banks with large market shares operating in more concentrated markets are early adopters, providing a direct support of the Schumpeterian hypothesis that market power enhances innovation.The views expressed here are those of the authors and do not necessarily reflect those of the Bank of Italy.     

≪Global dynamics and controls in an irregular economy model≫

The macroeconomic model of an irregular economy proposed by B. Contini, F. Cugno and M. Galeotti (1984) is extended by increasing the number of state variables and thus the dimension of the phase space for the relative dynamical system.By showing, through standard Liapunov methods, the non existence of closed non trivial orbits, the global attractivity of the equilibrium set is proved, under suitable boundary conditions.Control policies leading the economy to a desired equilibrium state are seen to be feasible, and central instruments which appear to be effective in this respect are briefly discussed.

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Riassunto Il lavoro estende un modello macroeconomico dell'economia irregolare che è stato proposto da B. Contini, F. Cugno e M. Galeotti nel 1984.Come nello schema originario la dimensione di ciascun settore economico (quello regolare e quello irregolare) dipende dall'andamento dei costi ad esso relativi, mentre il tasso di inflazione è legato ai prezzi ed alle quote dei due diversi settori.Noi non trattiamo, tuttavia, il differenziale tra i tassi di crescita della produttività,k, come una grandezza costante, e scriviamo, invece, una nuova equazione differenziale che ne descrive la dinamica.In questo modo si ottiene uno spazio delle fasi di dimensione tre che è stratificato da varietà invarianti di dimensione due. Ciascuna di queste varietà contiene esattamente un punto di equilibrio, che si prova essere un attrattore globale, sotto opportune condizioni al bordo.Dimostriamo, infine, che nell'ambito del nostro modello è formalemente possibile controllare il settore irregolare; questo ci porta al problema economico di quali politiche centrali siano atte a far conseguire un obbiettivo fissato relativamente alla dimensione della attività regolari ed irregolari in cui si articola il sistema.

     

Sulla dinamica dei processi di scambio monetari

In questa nota si propone una estensione del modello dinamico di economia monetaria di puro scambio sviluppato da D. Friedman in un lavoro recente [5]. Lo schema analitico mantiene il carattere non deterministico e non tâtonnement introdotto da S. Smale nello studio di processi transattivi [9]. Ammettendo che la merce usata nel sistema come moneta sia richiesta dagli agenti non solo sulla base delle sue caratteristiche fisiche, ma anche a partire dal ruolo istituzionale assolto, si prova che il processo economico converge ad una varietà di configurazioni finali che è strettamente più ampia dell'insieme degli equilibri walrasiani.     

Precautionary principle as a rule of choice with optimism on windfall gains and pessimism on catastrophic losses

The paper investigates a decision-making process involving both risk and ambiguity. Differently from existing papers [Basili, M., Chateauneuf, A., Fontini, F., 2005. Choices under ambiguity with familiar and unfamiliar outcomes, Theory and Decision 58, 195-207; Chichilnisky, G., 2000. Axiomatic approach to choice under uncertainty with catastrophic risks. Resources and Energy Economics 22, 221-231; Chichilnisky, G., 2002. In: El-Shaarawi, A.,H., Piegorsch, W.W. (Eds.), Catastropic Risks. Encyclopedia of Environmetrics, vol. 1. John Wiley & Sons, Ltd, Chichester, UK, pp. 274-279], we assume that, in a Choquet Expected Utility framework, the decision-maker is pessimistic with respect to unfamiliar (catastrophic) losses, optimistic with respect to unfamiliar (windfall) gains and ambiguity-neutral with respect to the familiar world. A representation of the decision-maker's choice is obtained that mimics the Restricted Bayes-Hurwicz Criterion. In this way a characterization of the Precautionary Principle is introduced for decision-making processes under ambiguity with catastrophic losses and/or windfall gains.     

The European Monetary Policy Responses During the Pandemic Crisis

This paper uses an event-based analysis to describe how the European Central Bank’s (ECB’s) policy responses to the pandemic crisis have affected the European financial and economic system. The result of our exercise, which is based on the examination of the main measures taken by the ECB during 2020, is that these responses have positively affected the European economic system by improving banks’ lending activity and by indirectly creating room for expansionary fiscal policies in the euro area’s high-debt countries that do not have fiscal capacity.

     

Disentangling (new) labour market divides: outsiders’ and globalization losers’ socio-economic risks in Europe

Quality & Quantity - In post-industrial and globalized economies, socio-economic risks have become ubiquitous for workers. Two segments of the labour force seem particularly exposed: namely,...