Stefano Marmi

When Micro Prudence Increases Macro Risk: The Destabilizing Effects of Financial Innovation, Leverage, and Diversification

By exploiting basic common practice accounting and risk-management rules, we propose a simple analytical dynamical model to investigate the effects of microprudential changes on macroprudential outcomes. Specifically, we study the consequence of the introduction of a financial innovation that allows reducing the cost of portfolio diversification in a financial system populated by financial institutions having capital requirements in the form of Value at Risk (VaR) constraint and following standard mark-to-market and risk-management rules. We provide a full analytical quantification of the multivariate feedback effects between investment prices and bank behavior induced by portfolio rebalancing in presence of asset illiquidity and show how changes in the constraints of the bank portfolio optimization endogenously drive the dynamics of the balance sheet aggregate of financial institutions and, thereby, the availability of bank liquidity to the economic system and systemic risk. The model shows that when financial innovation reduces the cost of diversification below a given threshold, the strength (because of higher leverage) and coordination (because of similarity of bank portfolios) of feedback effects increase, triggering a transition from a stationary dynamics of price returns to a nonstationary one characterized by steep growths (bubbles) and plunges (bursts) of market prices.

Modelling Systemic Price Cojumps with Hawkes Factor Models

Instabilities in the price dynamics of a large number of financial assets are a clear sign of systemic events. By investigating portfolios of highly liquid stocks, we find that there are a large number of high-frequency cojumps. We show that the dynamics of these jumps is described neither by a multivariate Poisson nor by a multivariate Hawkes model. We introduce a Hawkes one-factor model which is able to capture simultaneously the time clustering of jumps and the high synchronization of jumps across assets.

Evolution of Correlation Structure of Industrial Indices of US Equity Markets

We investigate the dynamics of correlations present between pairs of industry indices of US stocks traded in US markets by studying correlation based networks and spectral properties of the correlation matrix. The study is performed by using 49 industry index time series computed by K. French and E. Fama during the time period from July 1969 to December 2011 that is spanning more than 40 years. We show that the correlation between industry indices presents both a fast and a slow dynamics. The slow dynamics has a time scale longer than five years showing that a different degree of diversification of the investment is possible in different periods of time. On top to this slow dynamics, we also detect a fast dynamics associated with exogenous or endogenous events. The fast time scale we use is a monthly time scale and the evaluation time period is a 3 month time period. By investigating the correlation dynamics monthly, we are able to detect two examples of fast variations in the first and second eigenvalue of the correlation matrix. The first occurs during the dot-com bubble (from March 1999 to April 2001) and the second occurs during the period of highest impact of the subprime crisis (from August 2008 to August 2009).

Natural boundary for the susceptibility function of generic piecewise expanding unimodal maps

We consider the susceptibility function Psi(z) of a piecewise expanding unimodal interval map f with unique acim mu, a perturbation X, and an observable phi. Combining previous results (deduced from spectral properties of Ruelle transfer operators) with recent work of Breuer-Simon (based on techniques from the spectral theory of Jacobi matrices and a classical paper of Agmon), we show that density of the postcritical orbit (a generic condition) implies that Psi(z) has a strong natural boundary on the unit circle. The Breuer-Simon method provides uncountably many candidates for the outer functions of Psi(z), associated to precritical orbits. If the perturbation X is horizontal, a generic condition (Birkhoff typicality of the postcritical orbit) implies that the nontangential limit of the Psi(z) as z tends to 1 exists and coincides with the derivative of the acim with respect to the map (linear response formula). Applying the Wiener-Wintner theorem, we study the singularity type of nontangential limits as z tends to e^{i\omega}. An additional LIL typicality assumption on the postcritical orbit gives stronger results.

Collective synchronization and high frequency systemic instabilities in financial markets

We present some empirical evidence on the dynamics of price instabilities in financial markets and propose a new Hawkes modelling approach. Specifically, analysing the recent high frequency dynamics of a set of US stocks, we find that since 2001 the level of synchronization of large price movements across assets has significantly increased. We find that only a minor fraction of these systemic events can be connected with the release of pre-announced macroeconomic news. Finally, the larger is the multiplicity of the event—i.e. how many assets have swung together—the larger is the probability of a new event occurring in the near future, as well as its multiplicity. To reproduce these facts, due to the self- and cross-exciting nature of the event dynamics, we propose an approach based on Hawkes processes. For each event, we directly model the multiplicity as a multivariate point process, neglecting the identity of the specific assets. This allows us to introduce a parsimonious parametrization of the kernel of the process and to achieve a reliable description of the dynamics of large price movements for a high-dimensional portfolio.

There is only one KAM curve

We consider the standard family of area-preserving twist maps of the annulus and the corresponding KAM curves. Addressing a question raised by Kolmogorov, we show that, instead of viewing these invariant curves as separate objects, each of which having its own Diophantine frequency, one can encode them in a single function of the frequency which is naturally defined in a complex domain containing the real Diophantine frequencies and which is monogenic in the sense of Borel; this implies a remarkable property of quasianalyticity, a form of uniqueness of the monogenic continuation, although real frequencies constitute a natural boundary for the analytic continuation from the Weierstrass point of view because of the density of the resonances.

Bounded type interval exchange maps

Irrational numbers of bounded type have several equivalent characterizations. They have bounded partial quotients in terms of arithmetic characterization and in the dynamics of the circle rotation, the rescaled recurrence time to r-ball of the initial point is bounded below. In this paper, we consider how the bounded type condition of irrational is generalized into interval exchange maps.

Why Was USA Downgraded and Germany Not? A Market Dynamics Analysis

We investigate market-implied rating changes for AAA-rated sovereign issuers in the course of the Lehman and the Euro-sovereign crisis. Credit scores can be derived from the dynamics of CDS spread thanks to a time-dependent boundary model. They were successful in explaining rating changes for corporate issuers, but failed to predict the downgrade of USA to AA in August 2011, while Germany’s AAA rating was kept unchanged. We discuss this inconsistency in the light of the joint dynamics of both CDS and bond spreads. A downgrade is then explained through a signal of gradual creditworthiness deterioration across both markets.In Summer 2011 the CDS spread of most of European countries, Germany included, widened to unprecedented levels. However the joint dynamics of CDS and bond spread was not contradicting the USA downgrade. Conversely, the fly to quality in the Bund showed a clear indication of German credit quality enhancement, both in absolute terms and with respect to USA credit quality.This mixed signal can justify the retention of the AAA grade even from the perspective of market-implied ratings and calls for developing a comprehensive model. This should not be founded exclusively on CDS spreads, as most of the models discussed in the literature, but it should also be able to incorporate information implied by the bond market.

A Stylized Model for Long-Run Index Return Dynamics

We introduce a discrete-time model of stock index return dynamics grounded on the ability of Shiller’s Cyclically Adjusted Price-to-Earning ratio to predict long-horizon market performances. Specifically, we discuss a model in which returns are driven by a fundamental term and an autoregressive component perturbed by external random disturances. The autoregressive component arises from the agents’ belief that expected returns are higher in bullish markets than in bearish markets. The fundamental term, driven by the value towards which fundamentalists expect the current price should revert, varies in time and depends on the initial averaged price-to-earnings ratio. The actual stock price may deviate from the perceived reference level as a combined effect of an idyosyncratic noise component and local trends due to trading strategies. We demonstrate both analytically and by means of numerical experiments that the long-run behavior of our stylized dynamics agrees with empirical evidences reported in literature.

Sovereign Ratings Implied by Coupled CDS-Bond Market Data

We propose an approach to sovereign market implied ratings based on informations coming both from Credit Default Swap spreads and bond spreads in a unified way. Operationally speaking, we implement a Support Vector Machine type of selection in the plane CDS-bond. Our numerical results seem to confirm that introducing the bond dimension accounts for implied ratings more accurate and with greater predictive power with respect to the 1-dimensional CDS implied ratings.We propose an approach to sovereign market implied ratings based on informations coming both from Credit Default Swap spreads and bond spreads in a unified way. Operationally speaking, we implement a Support Vector Machine type of selection in the plane CDS-bond. Our numerical results seem to confirm that introducing the bond dimension accounts for implied ratings more accurate and with greater predictive power with respect to the 1-dimensional CDS implied ratings.