Instabilities in the price dynamics of a large number of financial assets are a clear sign of sys... more Instabilities in the price dynamics of a large number of financial assets are a clear sign of systemic events. By investigating a set of 20 high cap stocks traded at the Italian Stock Exchange, we find that there is a large number of multiple cojumps, i.e. minutes in which a sizable number of stocks displays a discontinuity of the price process. We show that the dynamics of these jumps is not described neither by a multivariate Poisson nor by a multivariate Hawkes model, which are unable to capture simultaneously the time clustering of jumps and the high synchronization of jumps across assets. We introduce a one factor model approach where both the factor and the idiosyncratic jump components are described by a Hawkes process. We introduce a robust calibration scheme which is able to distinguish systemic and idiosyncratic jumps and we show that the model reproduces very well the empirical behaviour of the jumps of the Italian stocks.
This paper investigates the degree of efficiency for the Moscow Stock Exchange. A market is calle... more This paper investigates the degree of efficiency for the Moscow Stock Exchange. A market is called efficient if prices of its assets fully reflect all available information. We show that the degree of market efficiency is significantly low for most of the months from 2012 to 2021. We calculate the degree of market efficiency by (i) filtering out regularities in financial data and (ii) computing the Shannon entropy of the filtered return time series. We developed a simple method for estimating volatility and price staleness in empirical data in order to filter out such regularity patterns from return time series. The resulting financial time series of stock returns are then clustered into different groups according to some entropy measures. In particular, we use the Kullback–Leibler distance and a novel entropy metric capturing the co-movements between pairs of stocks. By using Monte Carlo simulations, we are then able to identify the time periods of market inefficiency for a group o...
The interconnections between financial markets and macroeconomic stability of sovereigns is curre... more The interconnections between financial markets and macroeconomic stability of sovereigns is currently under the spot light. In fact, all members of the European Monetary Union (EMU) experienced in the past years some degree of economic distress caused by chain-reaction mechanisms; however, reactions to financial shocks differ greatly among them. The credit risk score attributed to a country by rating agencies express indeed also the resiliency to financial disturbances. The first goal of this work is to build a quantitative credit risk score that combines macroeconomic and financial variables, which can also help in explaining the country-specific reactions. We select as macroeconomic variables the primary fiscal deficit and the ratio public debt/GDP, that are also subject to limitations after the Maastricht Treaty (1992). We add market yields of government bonds, that provide a timely insight into financial markets’ expectations. Their trend is moreover at the origin of chain-reaction mechanisms: e.g. Greece’s default (debt restructuring) became unavoidable since the country debt was excluded from secondary market. We chose to follow the ideas of Minsky (1992) to connect these quantities by an economic model. In the government budget equation, we forecast future interest expenses thanks to the current market yield, so as to infer whether the state is a Ponzi debtor. Based on this, we define a non-linear credit-score, from which a default probability (PD) is derived. We compare it to the PD implied from the CDS market for a panel of EU countries and we assess whether a cointegration relationship exists between the two time series. In fact, the econometrics of integrated VARs provides long-run equilibrium relationship to be the natural economic interpretation of cointegrating relations (Johansen, 1995). We rely therefore on the existence of such a relation as an indicator of the country weakness in resist against financial shocks, since it shows how a temporary lack of public balance equilibrium affects market confidence in the long run.
One considers a system on \begin{document}$ \mathbb{C}^2 $\end{document} close to an invariant cu... more One considers a system on \begin{document}$ \mathbb{C}^2 $\end{document} close to an invariant curve which can be viewed as a generalization of the semi-standard map to a trigonometric polynomial with many Fourier modes. The radius of convergence of an analytic linearization of the system around the invariant curve is bounded by the exponential of the negative Brjuno sum of \begin{document}$ d\alpha $\end{document}, where \begin{document}$ d\in \mathbb{N}^* $\end{document} and \begin{document}$ \alpha $\end{document} is the frequency of the linear part, and the error function is non decreasing with respect to the smallest coefficient of the trigonometric polynomial.
Instabilities in the price dynamics of a large number of financial assets are a clear sign of sys... more Instabilities in the price dynamics of a large number of financial assets are a clear sign of systemic events. By investigating a set of 20 high cap stocks traded at the Italian Stock Exchange, we find that there is a large number of multiple cojumps, i.e. minutes in which a sizable number of stocks displays a discontinuity of the price process. We show that the dynamics of these jumps is not described neither by a multivariate Poisson nor by a multivariate Hawkes model, which are unable to capture simultaneously the time clustering of jumps and the high synchronization of jumps across assets. We introduce a one factor model approach where both the factor and the idiosyncratic jump components are described by a Hawkes process. We introduce a robust calibration scheme which is able to distinguish systemic and idiosyncratic jumps and we show that the model reproduces very well the empirical behaviour of the jumps of the Italian stocks.
This paper investigates the degree of efficiency for the Moscow Stock Exchange. A market is calle... more This paper investigates the degree of efficiency for the Moscow Stock Exchange. A market is called efficient if prices of its assets fully reflect all available information. We show that the degree of market efficiency is significantly low for most of the months from 2012 to 2021. We calculate the degree of market efficiency by (i) filtering out regularities in financial data and (ii) computing the Shannon entropy of the filtered return time series. We developed a simple method for estimating volatility and price staleness in empirical data in order to filter out such regularity patterns from return time series. The resulting financial time series of stock returns are then clustered into different groups according to some entropy measures. In particular, we use the Kullback–Leibler distance and a novel entropy metric capturing the co-movements between pairs of stocks. By using Monte Carlo simulations, we are then able to identify the time periods of market inefficiency for a group o...
The interconnections between financial markets and macroeconomic stability of sovereigns is curre... more The interconnections between financial markets and macroeconomic stability of sovereigns is currently under the spot light. In fact, all members of the European Monetary Union (EMU) experienced in the past years some degree of economic distress caused by chain-reaction mechanisms; however, reactions to financial shocks differ greatly among them. The credit risk score attributed to a country by rating agencies express indeed also the resiliency to financial disturbances. The first goal of this work is to build a quantitative credit risk score that combines macroeconomic and financial variables, which can also help in explaining the country-specific reactions. We select as macroeconomic variables the primary fiscal deficit and the ratio public debt/GDP, that are also subject to limitations after the Maastricht Treaty (1992). We add market yields of government bonds, that provide a timely insight into financial markets’ expectations. Their trend is moreover at the origin of chain-reaction mechanisms: e.g. Greece’s default (debt restructuring) became unavoidable since the country debt was excluded from secondary market. We chose to follow the ideas of Minsky (1992) to connect these quantities by an economic model. In the government budget equation, we forecast future interest expenses thanks to the current market yield, so as to infer whether the state is a Ponzi debtor. Based on this, we define a non-linear credit-score, from which a default probability (PD) is derived. We compare it to the PD implied from the CDS market for a panel of EU countries and we assess whether a cointegration relationship exists between the two time series. In fact, the econometrics of integrated VARs provides long-run equilibrium relationship to be the natural economic interpretation of cointegrating relations (Johansen, 1995). We rely therefore on the existence of such a relation as an indicator of the country weakness in resist against financial shocks, since it shows how a temporary lack of public balance equilibrium affects market confidence in the long run.
One considers a system on \begin{document}$ \mathbb{C}^2 $\end{document} close to an invariant cu... more One considers a system on \begin{document}$ \mathbb{C}^2 $\end{document} close to an invariant curve which can be viewed as a generalization of the semi-standard map to a trigonometric polynomial with many Fourier modes. The radius of convergence of an analytic linearization of the system around the invariant curve is bounded by the exponential of the negative Brjuno sum of \begin{document}$ d\alpha $\end{document}, where \begin{document}$ d\in \mathbb{N}^* $\end{document} and \begin{document}$ \alpha $\end{document} is the frequency of the linear part, and the error function is non decreasing with respect to the smallest coefficient of the trigonometric polynomial.
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Papers by Stefano Marmi