Margin Exceedences for European Stock Index Futures Using Extreme Value Theory

Cotter, John

doi:10.2139/ssrn.996071

Cited by 40 publications

(45 citation statements)

References 28 publications

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“…As shown in equation (20), the VaR is an a¢ne function of the conditional variance of the P&L, denoted h t . Di¤erently, the sVaR depends on a conditional variance of the P&L measured over a particularly volatile period, denoted H t :…”

Section: Bank Stressed Varmentioning

confidence: 99%

The Risk Map: A new tool for validating risk models

Colletaz

Hurlin

Pérignon

2013

Journal of Banking & Finance

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This paper presents a new method to validate risk models: the Risk Map. This method jointly accounts for the number and the magnitude of extreme losses and graphically summarizes all information about the performance of a risk model. It relies on the concept of a super exception, which is dened as a situation in which the loss exceeds both the standard Value-at-Risk (VaR) and a VaR dened at an extremely low coverage probability. We then formally test whether the sequences of exceptions and super exceptions are rejected by standard model validation tests. We show that the Risk Map can be used to validate market, credit, operational, or systemic risk estimates (VaR, stressed VaR, expected shortfall, and CoVaR) or to assess the performance of the margin system of a clearing house.JEL classication: G21, G28, G32

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Section: Bank Stressed Varmentioning

confidence: 99%

The Risk Map: A new tool for validating risk models

Colletaz

Hurlin

Pérignon

2013

Journal of Banking & Finance

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“…For example, Longin (1996) and Longin and Solnik (2001) studied properties of extremes of equity market returns; Longin (1999) and Cotter (2001) considered futures markets, and in particular margin requirements and exceedances. Galbraith and Zernov (2004) studied changes in the tail index of equity returns in the context of evolving elements of market architecture such as circuit breakers.…”

Section: Introductionmentioning

confidence: 99%

Extreme dependence in the NASDAQ and S&P 500 composite indexes

Galbraith

Zernov²

2009

Applied Financial Economics

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Dependence among large observations in equity markets is usually examined using secondmoment models such as those from the GARCH or SV classes. Such models treat the entire set of returns, and tend to produce very similar estimates on the major equity markets, with a sum of estimated GARCH parameters, for example, slightly below one. Using dependence measures from extreme value theory, however, it is possible to characterize dependence among only the largest (or largest negative) financial returns; these alternative characterizations of clustering have important applications in risk management. In this paper we compare the NASDAQ and S&P in this way, and implement tests which can be used for the null hypothesis of the same degree of extreme dependence. Although GARCH-type characterizations of second-moment dependence in the two markets produce similar results, the same is not true in the extremes: we find significantly more extreme dependence in the NASDAQ returns. More generally, the study of extreme dependence may reveal contrasts which are obscured when examining the conditional second moment.

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“…ii The approach has also been used in a multivariate setting examining extreme spillovers between markets 8 and estimating extreme correlations for bull and bear markets 9 . property has been documented for the extreme returns of many financial time series, such as index returns 11 , single equities (Danielsson and de Vries, 2000) 12 , foreign exchange (Huisman et al, 2001) 13 and derivatives (Cotter, 2001) 2 . The property indicates the propensity for financial time series to exhibit upside and downside returns of very large magnitude relative to the normal distribution for given probability levels.…”

Section: Theory and Estimation Methodsmentioning

confidence: 99%

Extreme global equity market risk

Cotter

Dowd²

2011

J Deriv Hedge Funds

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Publication AbstractExtreme asset price movements appear to be more pronounced over time and have major consequences for an economy's financial stability and monetary policies. This paper investigates the extreme behaviour of equity market returns and quantifies the probabilities of these losses. Taking fourteen major equity markets the study illustrates similarities and divergences in the tail returns from around the world. To do so, it applies extreme value theory to equity indices representing American, Asian and European markets. The paper finds that all markets tail realisations are adequately modelled with the fat-tailed Fréchet distribution.Furthermore tail realisations associated with the downside of a distribution are greater than those associated with the upside, and extreme returns for Asian markets are usually larger than their European and American counterparts. JEL classification: G1; G10.

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Margin Exceedences for European Stock Index Futures Using Extreme Value Theory

Cited by 40 publications

References 28 publications

The Risk Map: A new tool for validating risk models

The Risk Map: A new tool for validating risk models

Extreme dependence in the NASDAQ and S&P 500 composite indexes

Extreme global equity market risk

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