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Systemic risk
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===SRISK=== A financial institution represents a systemic risk if it becomes undercapitalized when the financial system as a whole is undercapitalized. In a single risk factor model, Brownlees and Engle <ref>Brownlees, C.T., Engle, R.F., 2010. Volatility, correlation and tails for systemic risk measurement, {{ssrn|1611229}}.</ref> build a systemic risk measure named SRISK. SRISK can be interpreted as the amount of capital that needs to be injected into a financial firm as to restore a certain form of minimal capital requirement. SRISK has several nice properties: SRISK is expressed in monetary terms and is, therefore, easy to interpret. SRISK can be easily aggregated across firms to provide industry and even country specific aggregates. Last, the computation of SRISK involves variables which may be viewed on their own as risk measures. These are the size of the financial firm, the leverage (ratio of assets to market capitalization), and a measure of how the return of the firm evolves with the market (some sort of time varying conditional [[Beta (finance)|beta]] but with emphasis on the tail of the distribution). Whereas the initial Brownlees and Engle model is tailored to the US market, the extension by Engle, Jondeau, and Rockinger<ref>Engle, R.F., Jondeau, E., Rockinger, M., 2012. Systemic Risk in Europe. {{ssrn|2192536}}.</ref> is more suitable for the European markets. One factor captures worldwide variations of financial markets, another one the variations of European markets. This extension allows for a country-specific factor. By accounting for different factors, one captures the notion that shocks to the US or Asian markets may affect Europe, but also that bad news within Europe (such as the news about a potential default of one of the countries) matters for Europe. Also, there may be country specific news that does not affect Europe or the US, but matters for a given country. Empirically the last factor is less relevant than the worldwide or European factor. Since SRISK is measured in terms of currency, the industry aggregates may also be related to [[Gross Domestic Product]]. As such one obtains a measure of domestic, systemically important banks. The SRISK Systemic Risk Indicator is computed automatically on a weekly basis and made available to the community. For the US model, SRISK and other statistics may be found under the [http://vlab.stern.nyu.edu/ Volatility Lab of NYU Stern School] website and for the European model under the [http://www.crml.ch/ Center of Risk Management (CRML)] website of HEC Lausanne. ====Pair/vine copulas==== A [[vine copula]] can be used to model systemic risk across a portfolio of financial assets. One methodology is to apply the Clayton Canonical Vine Copula to model asset pairs in the vine structure framework. As a Clayton copula is used, the greater the degree of asymmetric (i.e., left tail) dependence, the higher the Clayton copula parameter. Therefore, one can sum up all the Clayton Copula parameters, and the higher the sum of these parameters, the greater the impending likelihood of systemic risk. This methodology has been found to detect spikes in the US equities markets in the last four decades capturing the Oil Crisis and Energy Crisis of the 1970s, Black Monday and the Gulf War in the 1980s, the Russian Default/LTCM crisis of the 1990s, and the Technology Bubble and Lehman Default in the 2000s.<ref>{{Cite journal|last=Low|first=Rand |date=2017-05-11|title=Vine copulas: modelling systemic risk and enhancing higher-moment portfolio optimisation.|journal=Accounting & Finance|volume=58 |pages=423β463|doi=10.1111/acfi.12274 |issn=1467-629X|doi-access=free}}</ref> Manzo and Picca<ref>{{cite journal|last1=Manzo|first1=Gerardo|last2=Picca|first2=Antonio|title=The Impact of Sovereign Shocks|year=2018|journal=Management Science, Forthcoming|ssrn=2524991}}</ref> introduce the t-Student Distress Insurance Premium (tDIP), a copula-based method that measures systemic risk as the expected tail loss on a credit portfolio of entities, in order to quantify sovereign as well as financial systemic risk in Europe.
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