Banks' resilience against economic shocks: theoretical and empirical essays

The complete research consists of two independent section of financial studies. The first section is a joint work with Vittoria Cerasi which involves the theoretical studies of interlocking directorates effect under macroeconomic shock in banking. While the second section involves both theoretical and empirical studies about backtesting VaR and expectiles with realized scores. Interlocking directorates occur whenever an executive in one board sits also in the board of another organization. Usually interlocks are seen as a collusive device. Despite legal restrictions on interlocks for antitrust reasons, they remain quite common in the financial sector. In this paper the effect of interlocking directorates is investigated for the special case of banks. We delineate a theoretical model that illustrates cost and benefit of interlocking directorates and compare it to the case of independent boards. The setup of the model is that of imperfect information, since the quality of the board is imperfectly known to rivals. We study the conditions for a Perfect Bayesian equilibrium to exist with interlocking directorates. Furthermore, we show that two symmetric equilibria arise: one with interlocking directorates and one with independent boards. The equilibrium with interlocking may be preferable from a welfare point of view when coordination is prohibited by the antitrust law. This could be particularly relevant for banks located in independent markets but exposed to common macroeconomic shocks. The research moves in the following part. This part study the backtesting VaR and expectiles with realized scores. Traditionally, backtesting is a process that compare risk measure forecast with realized financial losses over a period of time. In this joint work with F. Bellini and I. Negri we are concerned on the problem how to backtest the choice of the risk measure with scoring function. Some statistical functionals such as the quantiles and the expectiles arise naturally as the minimisers of the expected value of a scoring function, a property that is called elicitability. As a consequence, these functional may also be defined through a first order condition, that requires that the expected value of a suitable identification function is null. Realised scores and realised identification functions are defined as the empirical counterpart of expected scores and expected identification functions.n this work, we investigate the asymptotic distribution of the quantile and expectile scoring functions in the case of normal and uniform i.i.d. samples. We suggest a backtesting methodology that rejects the forecasting model under scrutiny if the scoring function is too big in comparison with the theoretical distribution. To take into account departures from independence we first compute the probability integral transform, as it has already been done e.g. in Kerkhof and Melenberg (2004). Our approach is close to approach of Fissler et al. (2016), where they study a comparative backtesting. Nolde and Ziegel (2016) differentiate between traditional backtesting and comparative backtesting, while we provide an absolute backtesting. We compare our technique with existing approaches both on real and simulated data and the results seems to indicate an higher empirical power againts certain types of misspecification. We are running similar computation for the backtesting of the Expected Shortfall, by means of the bivariate scoring functions introduced by Fissler and Ziegel (2016), Acerbi and Szekely (2014).