Modelling Extremal Events

Embrechts, Paul; Klüppelberg, Claudia; Mikosch, Thomas

doi:10.1007/978-3-642-33483-2

Cited by 3,806 publications

(1,500 citation statements)

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“…Both the decrease rate and the short correlation range ensure that the distribution of converge to a Gumbel distribution [50][51] However the convergence may be slow as discussed above ( figure 12a). This is the reason why we restricted the range of β in figure 11 to (0-4).…”

Section: 2the Linear Correlation Between Neighbouring Spacingsmentioning

confidence: 95%

Nearest-neighbour spacing distributions of the β-Hermite ensemble of random matrices

Caër¹,

Male²,

Delannay³

2007

Physica A: Statistical Mechanics and its Applications

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Section: 2the Linear Correlation Between Neighbouring Spacingsmentioning

confidence: 95%

Nearest-neighbour spacing distributions of the β-Hermite ensemble of random matrices

Caër¹,

Male²,

Delannay³

2007

Physica A: Statistical Mechanics and its Applications

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“…We outline the fundamental aspects of each method. Further details can be found in Embrechts, Klüppelberg and Mikosch (1997) and Reiss and Thomas (1997).…”

Section: Univariate Methodsmentioning

confidence: 99%

“…Loretan and Phillips (1994) use evt to study the existence of moments of financial returns, and Longin (1996) shows that the tails of stock market returns belong to the Fréchet class. Embrechts, Klüppelberg and Mikosch (1997) provide a summary of general evt results and comprehensive references. Diebold, Schuerman and Stroughair (1998) sketch a number of pitfalls associated with the application of evt techniques to financial data.…”

Section: Introductionmentioning

confidence: 99%

Modelling Extreme-Value Dependence in International Stock Markets

2002

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In the finance literature, cross-sectional dependence in extreme returns of risky assets is often modelled implicitly assuming an asymptotically dependent structure. If the true dependence structure is asymptotically independent then current modelling approaches will lead to an over-estimation of the risk of simultaneous extreme events. We use two simple nonparametric measures to identify and quantify the tail dependence among stock returns in five international stock markets. We show that there is strong evidence in favour of asymptotically independent models for the tail structure of stock market returns, and that most of the extremal dependence is due to heteroskedasticity in stock returns processes. Using a range of volatility filters, we find that tail index and tail dependence can be partially captured by models for heteroskedasticity. We find there is no clear reason to prefer one volatility filter over another.

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“…by assumption t 2 (t) → ∞ and the central limit theorem for the renewal process (see, e.g., Theorem 2.5.13 in Embrechts et al (1997)):…”

Section: Proof Write |K−λt|>ε(t)λtmentioning

confidence: 99%

“…Using the property of subexponential distribution B (see, e.g., Lemma 1.3.5 in Embrechts et al (1997)) we have that for each > 0 there exists a constant K( ) such that…”

Section: Proof Write |K−λt|>ε(t)λtmentioning

confidence: 99%