Systemic risk plays a pivoltal role in financial market and stability, but despite the importance of having a comprehensive knowledge of this phenomenon, the literature fails in providing an exhaustive understanding about measuring the effects and magnitude of what a systemic failure implies both from a horizontal perspective (spreading of the crisis across institutions, banks and firms) and from a vertical perspective (how deep the crisis is, and which agents will be involved, from big investment funds to private investors). The paper reviews the most recent literature on the issue and contributes to the debate. 


Bank failures and subsequent macroeconomic breakdowns constitute a threat for the overall financial stability, and at the same time, a financial dislocation with incalculable consequences for both the financial and real economy. The de Larosière Group (2009) on financial supervision in the EU has analyzed many drivers as causes of the recent turmoil in the financial system. The first concerns the failure in risk assessment procedures, both from the side of financial banks and firms, and from the side of institutions that have been established with the mandate to guarantee efficient regulation and supervision (Basel I and II) 1. The overestimation of regulators of the ability of the financial firms to manage situations of financial distress, and the corresponding underestimation of minimum capital requirements, have represented a weak factor that has to be considered for a full understanding of the macroeconomic forces of financial soundness. Secondly, the exponential development of derivative instruments has complicated the evaluation of risky assets in any field of financial engineering, shedding light on the unreliability of current model-based risk assessments (i.e. CAPM and VaR 2). It has contributed to generate a parallel hidden banking system with reduced information about the size or origination of credit risks, highlighting a lack of transparency in many segments of the international financial system. In this regard, a special role has been played by the sudden growth of Over-the-Counter credit derivatives markets. Even if these markets were initially envisaged as a powerful risk management instrument mitigating the likely negative states of nature, in reality they have spread the threat of a systemic risk. Thirdly, the "originate-to-distribute" model has created huge possibilities and incentives for speculators, by diverting attention from the solvency capacity of third-party counterparts (BIS, 2009).
Despite the importance of having a comprehensive knowledge of this phenomenon, the literature fails in providing an exhaustive understanding about measuring the effects and magnitude of what a systemic failure implies both from a horizontal perspective (spreading of the crisis across institutions, banks and firms) and from a vertical perspective (how deep the crisis is, and which agents will be involved, from big investment funds to private investors). Furthermore, considering the lack of consensus of what a systemic risk is (see also"On the Different Meanings of Systemic Risk") and the difficulty in detecting an independent and clear measure suitable for any scenario and market, there are a distinct number of reliable quantitative indicators 3 utilised to measure the first signs of financial distress.
In this contest, we propose a dual classification to study the principal measurement tools of systemic risk. We opted for a different choice from that recently proposed in Billio et al. (2010), as we consider that the contagion among banks and the subsequent spillover effects coming from the insolvent bank can be classified in one category in order to have a whole understanding of this topic. Then we carried out our review of systemic risk measures in two broad categories: 
a)The first group focused on monitoring traditional macroeconomic indicators of financial soundness and stability;
b)The second group analysed the interlinkages between financial institutions through the analysis of the financial institutions' assets.
The first group of contributions relied on bank capital ratios and bank liabilities showing that aggregate macroeconomic indicators can provide a valid and useful instrument to predict systemic risk threat. Through the study of macroeconomic fundamentals, Gonzalez-Hermosillo et al. (1997), Gorton (1998) and Gonzalez-Hermosillo (1999) proved the evidence supporting the functioning of macro analysis in estimating systemic risk. More recently, Bhansali et al. (2008) derived the "systemic credit risk" variable from index credit derivatives and found that systemic risk during the 2007-2009 financial crisis showed a double value as compared to May 2005. De Nicolò and Lucchetta (2010) firstly used a dynamic factor model to work out joint forecasts of indicators of systemic real risk and systemic financial risk, and secondly they elaborated stress-tests of these indicators as impulse responses to structurally identifiable shocks. The use of aggregate indicators, if on one side it looks like the most suitable instrument for systemic risk assessment, on the other side illustrates its limitations for the infrequent character of the data under analysis. Macroeconomic indicators are characterised by monthly observations and are unreliable in capturing market-tensions released by sudden news and unexpected events, that, as the recent financial crisis has illustrated, can develop very rapidly with dramatic consequences on capital markets. Furthermore, by focusing on broad drivers of the financial system, this approach is bounded by the scarce information about the state of individual financial institutions, in particular about interlinkages between institutions.
The second group analysed the interlinkages between financial institutions as well as exposures among banks that through their business can influence each other in situations of financial distress. De Bandt and Hartmann (2000) provided an interesting survey of this category of studies. A more recent contribution was given by Lehar (2005), assessing the probability that a certain number of banks within a time period go bankrupt due to the decreasing of their asset value below a well-defined liability value. This view comes from the structural model by Merton (1974) wherein a bank’s default occurs when the asset banking values stand below a given threshold value.4 Adrian and Brunnermeier (2009) defined CoVaR as the VaR of financial institutions conditional on other institutions that experience, at the same time, financial distress. De Nicolò and Lucchetta (2009) investigated the transmission channels and contagion effects of certain shocks between the macroeconomy, financial markets and intermediaries. Huang et al. (2009) used as a proxy of systemic risk the price of insuring a dozen of the major US banks against financial turmoil by using both ex-ante bank default probabilities and forecasted asset-returns correlations. As the recent financial crisis has underscored, the need to understand the interlinkages between financial firms and the use of aggregate indicators is of crucial importance in order to construct better macro prudential indicators for policy makers and regulators and, at the same time, to have a deep understanding of the key drivers of systematic financial risk. For this purpose, the analysis of interlinkages between financial institutions is of key importance, both from a domestic and international point of view. With regard to this, the IMF (2009) surveyed four different methods to assess interlinkages between financial institutions:
-The network approach: here the interbank market spreads the transmission of financial stress through the banking system. Allen and Babus (2008) stated that network analysis is the best approach to lead an in-depth analysis of systemic risk, as it allows the regulator to analyse not only the fulcrum of the problem, but also the spillover effects from direct financial linkages 5through the construction of a matrix of inter-institution exposures that includes gross exposures among financial institutions (both national and international).
-The co-risk model (or co-movement risk model): in this specification, the probability of default of one institution is directly linked to the default risk of another institution. As underlined in Brunnermeier et al. (2009, p.5), "It may be that the best way to assess the implications of endogenous co-risk measures that measure the increase in overall risk after conditioning on the fact that one bank is in trouble". Empirical studies during the past ten years, such as de Vries et al. (2001), Longin and Solnik (2001) and Chan-Lau (2004) found a clear evidence that co-movement between financial variables is stronger during troubled times than during normal times.
-The distress dependence matrix studies the probability of default of a pair of banks, by taking into account a panel of financial banks. Through this method, it is possible to assess the probability of a financial institution experiencing distress conditional on another institution that shows clear signs of financial troubles. Goodhart and Segoviano (2008) offered a brilliant contribution to this technique.
-The default intensity model is able to capture the probability of default of a large part of financial institutions through linkages between some institutions. These kinds of models are worked out in terms of default rate jumps that occur at failure events, reflecting the increased likelihood of further events due to spillover effects. In this regard, Giesecke and Kim (2009) captured the clustering of the economy-wide default events as represented by the fitted intensity. 
Notwithstanding the insightful IMF classification, there are still substantial empirical contributions that deserve to be included in this analysis, even if it is not possible to specify them in the above four categories. 
Prices of financial assets, interest rates, financial stocks and flows represent good proxies as indicators of systemic risk. Their characteristics of being continuously available on the market with the capacity of representing the mirror of firm and banking performances make these variables valuable tools of systemic risk measurement. In this contest, Bartram et al. (2005) proposed three different approaches to estimate systemic risk. The first methodology assessed the risk of a systemic failure by observing the market reaction to global financial shocks for a subset of banks that are not directly exposed 6 to the shock. Stock market reactions of unexposed bank to the shock will be interpreted as a measure of systemic risk. The second approach was given by an assessment of the default probabilities of banks during the time of crisis. In order to estimate the default probabilities, they took into consideration a structural model, an idea developed by Merton (1974), of default estimated from an observed series of equity prices. In the third and last approach, they followed the estimation procedure applied by Duan (2000), Duan et al. 7 (2003), and Camara 8 (2004) by assessing systemic risk in the banking system through the bank default probabilities implied in their equity option prices. 
One of the most recent contributions of this class of indicators is provided by Capuano (2008) by developing a framework to derive a market-based measure of probability of default. This probability of default is defined as the probability that the value of the underlying asset will fall below a given threshold value that constitutes the default barrier itself. In contrast to Merton’s (1974) work, Capuano (2008) does not fix any predetermined ad-hoc default barrier, but it is rather endogenously determined.
Using a VaR approach, Acharya, et al. (2010), defined systemic risk as the likelihood of experiencing cumulative losses in a financial system that exceed that predicted by the VaR model. Furthermore, they proposed a tax (fee) that would require two components: (i) a component directly linked to the institution-risk and representing the expected loss on its guaranteed liabilities, and (ii) a systemic-risk component; namely, the risk is measurable when the financial sector becomes undercapitalised.
1As expressed in Acharya et al. (2010) "Basel I and Basel II are designed to limit each institution's risk seen in isolation; they are not sufficiently focused on systemic risk even though systemic risk often is the rationale provided for such regulation".
2The CAPM (Capital Asset Pricing Model), is a model able to describe the relationship between risk and expected return that is used in the price of risky securities. For an exhaustive explanation about CAPM, see Jensen, M, C., Balck, F., and Scholes, M.S "The Capital Asset Pricing Model: Some Empirical Tests" Studies in The Theory of Capital Markets". Praeger Publishers Inc., 1972. 
3Despite the fact that a major focus of the literature on systemic risk is focused on quantitative measures, there are also some contributions that take into consideration qualitative measuring instruments (Nelson et al.2005). For qualitative information tools we mean formal surveys of investors and bank senior loan officers, and informal contacts with market participants. In particular, considering the short amount of time available for decision making in the investment banking sector, this qualitative information assumes a remarkable connotation when unexpected events come up quickly, and there is no time to wait for an official response from quantitative surveys and analyses. 
4These models use option prices to approach credit risk by measuring on equity markets. See also KMVmodels.
5For a comprehensive survey of the literature, see Upper (2007).
6Bertrand et al. (2005) argued that in efficient capital markets, negative information (as 9/11) will affect bank performances that are exposed to the events in question. Unexposed banks will be unaffected by these effects. 
7Duan et al. (2003) derived a maximum-likelihood approach where the likelihood function for the equity value of the firms is derived in a structural model framework. Through maximizing this function, it is possible to obtain the implied default probabilities of the firm. 
8Camara (2004) developed an option pricing model in which asset prices follow a geometric random walk but may jump to zero (bankruptcy) with a finite probability distribution.
Editor: Claudio DICEMBRINO