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17
Extreme Correlation of International Equity Markets
 Journal of Finance
, 2001
"... Testing the hypothesis that international equity market correlation increases in volatile times is a difficult exercise and misleading results have often been reported in the past because of a spurious relationship between correlation and volatility. This paper focuses on extreme correlation, that i ..."
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Cited by 245 (0 self)
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Testing the hypothesis that international equity market correlation increases in volatile times is a difficult exercise and misleading results have often been reported in the past because of a spurious relationship between correlation and volatility. This paper focuses on extreme correlation, that is to say the correlation between returns in either the negative or positive tail of the multivariate distribution. Using “extreme value theory ” to model the multivariate distribution tails, we derive the distribution of extreme correlation for a wide class of return distributions. Using monthly data on the five largest stock markets from 1958 to 1996, we reject the null hypothesis of multivariate normality for the negative tail, but not for the positive tail. We also find that correlation is not related to market volatility per se but to the market trend. Correlation increases in bear markets, but not in bull markets.
Empirical properties of asset returns: stylized facts and statistical issues
 Quantitative Finance
, 2001
"... We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then des ..."
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Cited by 188 (3 self)
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We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then described: distributional properties, tail properties and extreme fluctuations, pathwise regularity, linear and nonlinear dependence of returns in time and across stocks. Our description emphasizes properties common to a wide variety of markets and instruments. We then show how these statistical properties invalidate many of the common statistical approaches used to study financial data sets and examine some of the statistical problems encountered in each case.
Multivariate Extremes, Aggregation and Risk Estimation
, 2000
"... We briefly introduce some basic facts about multivariate extreme value theory and present some new results regarding finite aggregates and multivariate extreme value distributions. Based on our results high frequency data can considerably improve quality of estimates of extreme movements in fina ..."
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Cited by 25 (0 self)
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We briefly introduce some basic facts about multivariate extreme value theory and present some new results regarding finite aggregates and multivariate extreme value distributions. Based on our results high frequency data can considerably improve quality of estimates of extreme movements in financial markets. Secondly we present an empirical exploration of what the tails really look like for four foreign exchange rates sampled at varying frequencies. Both temporal and spatial dependence is considered. In particular we estimate the spectral measure, which along with the tail index, completely determines the extreme value distribution. Lastly we apply our results to the problem of portfolio optimisation or risk minimization. We analyze how the expected shortfall and VaR scale with time horizon and find that this scaling is not by a factor of square root of time as is frequently used, but by a different power of time. We show that the accuracy of risk estimation can be drast...
Multivariate extremes and the aggregation of dependent risks: Examples and counterexamples
 Extremes, 2008. ISSN 13861999 (Print) 1572915X (Online). URL http://www.springerlink.com/content/ 102890/?Content+Status=Accepted
"... Properties of risk measures for extreme risks have become an important topic of research. In the present paper we discuss sub and superadditivity of quantile based risk measures and show how multivariate extreme value theory yields the ideal modeling environment. Numerous examples and counterexamp ..."
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Cited by 18 (7 self)
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Properties of risk measures for extreme risks have become an important topic of research. In the present paper we discuss sub and superadditivity of quantile based risk measures and show how multivariate extreme value theory yields the ideal modeling environment. Numerous examples and counterexamples highlight the applicability of the main results obtained.
An Application of Extreme Value Theory for Measuring Financial Risk
, 2006
"... Assessing the probability of rare and extreme events is an important issue in the risk management of financial portfolios. Extreme value theory provides the solid fundamentals needed for the statistical modelling of such events and the computation of extreme risk measures. The focus of the paper is ..."
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Cited by 15 (0 self)
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Assessing the probability of rare and extreme events is an important issue in the risk management of financial portfolios. Extreme value theory provides the solid fundamentals needed for the statistical modelling of such events and the computation of extreme risk measures. The focus of the paper is on the use of extreme value theory to compute tail risk measures and the related confidence intervals, applying it to several major stock market indices.
An Application of Extreme Value Theory for Measuring Risk
, 2003
"... Many fields of modern science and engineering have to deal with events which are rare but have significant consequences. Extreme value theory is considered to provide the basis for the statistical modelling of such extremes. The potential of extreme value theory applied to financial problems has onl ..."
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Cited by 6 (0 self)
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Many fields of modern science and engineering have to deal with events which are rare but have significant consequences. Extreme value theory is considered to provide the basis for the statistical modelling of such extremes. The potential of extreme value theory applied to financial problems has only been recognized recently. This paper aims at introducing the fundamentals of extreme value theory as well as practical aspects for estimating and assessing statistical models for tailrelated risk measures.
Strategic LongTerm Financial Risks: Single Risk Factors
 Issue 12, ISSN 09266003
, 2005
"... Abstract. The question of the measurement of strategic longterm financial risks is of considerable importance. Existing modelling instruments allow for a good measurement of market risks of trading books over relatively small time intervals. However, these approaches may have severe deficiencies if ..."
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Cited by 4 (3 self)
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Abstract. The question of the measurement of strategic longterm financial risks is of considerable importance. Existing modelling instruments allow for a good measurement of market risks of trading books over relatively small time intervals. However, these approaches may have severe deficiencies if they are routinely applied to longer time periods. In this paper we give an overview on methodologies that can be used to model the evolution of risk factors over a oneyear horizon. Different models are tested on financial time series data by performing backtesting on their expected shortfall predictions. 1
Extremal Dependence between Return Risk and Liquidity Risk: an Analysis for the Swiss Market
, 2002
"... We study the extremal dependence of market and liquidity risk, the former being measured through the market return and the latter being measured through the relative bidask spread. We apply a nonparametrical approach to measure bivariate exceedance probabilities and the respective dependence funct ..."
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Cited by 3 (0 self)
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We study the extremal dependence of market and liquidity risk, the former being measured through the market return and the latter being measured through the relative bidask spread. We apply a nonparametrical approach to measure bivariate exceedance probabilities and the respective dependence function. Our analysis for the Swiss Market indicates moderate tail dependence in that roughly 10 % of the exceedances of the 99 % quantile are coexceedances. As our hypothesis tests for independence are rejected for confidence levels of 5 % and 1 % in almost all cases, we conclude that extreme dependence between negative market returns and liquidity is existing in the empirical data and may be relevant for firmwide risk management. In addition, we test for causality and find decreasing extremal dependence when adding both positive and negative lags, respectively.
Portfolio selection with heavy tails
 Journal of Empirical Finance
, 2007
"... Consider the portfolio problem of choosing the mix between stocks and bonds under a downside risk constraint. Typically stock returns exhibit fatter tails than bonds corresponding to their greater downside risk. Downside risk criteria like the safety …rst criterion therefore often select corner solu ..."
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Cited by 3 (0 self)
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Consider the portfolio problem of choosing the mix between stocks and bonds under a downside risk constraint. Typically stock returns exhibit fatter tails than bonds corresponding to their greater downside risk. Downside risk criteria like the safety …rst criterion therefore often select corner solutions in the sense of a bonds only portfolio. This is due to a focus on the asymptotically dominating …rst order Pareto term of the portfolio return distribution. We show that if second order terms are taken into account, a balanced solution emerges. The theory is applied to empirical examples from the literature. Key words: safety …rst, heavy tails, portfolio diversi…cation; JEL
Strategic LongTerm Financial Risks The OneDimensional Case
, 2003
"... Abstract. The development of a methodology that could be used for the measurement of strategic longterm financial risks is becoming an important task. Existing modelling instruments allow for a good measurement of market risks of trading books over relatively small time intervals. However, these ap ..."
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Cited by 2 (0 self)
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Abstract. The development of a methodology that could be used for the measurement of strategic longterm financial risks is becoming an important task. Existing modelling instruments allow for a good measurement of market risks of trading books over relatively small time intervals. However, these approaches might have some severe deficiencies if they are applied to longer time periods. In this paper we give an overview on methodologies that are proposed to model the evolution of risk factors over a long horizon. We investigate in detail the statistical properties and the behaviour of financial time series at different frequencies. Then, we test the different models on these data by backtesting expected shortfall predictions.