Slow Variation With Remainder: Theory and Applications

Goldie, Charles M.; Smith, Richard L.

doi:10.1093/qmath/38.1.45

Cited by 186 publications

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“…Its asymptotic normality has been shown by, e.g., Goldie and Smith (1987) or Hall (1990), for which they obtain the variance Var(γ) = γ 2 / k Certainly, in applications the 'true' value γ is replaced with the estimateγ. The moment coverage ratios relate toγ rather than the Hill estimator 1/γ itself.…”

Section: Resultsmentioning

confidence: 99%

Structural stochastic volatility in asset pricing dynamics: Estimation and model contest

Franke

Westerhoff

2012

Journal of Economic Dynamics and Control

197

186

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In the framework of small-scale agent-based financial market models, the paper starts out from the concept of structural stochastic volatility, which derives from different noise levels in the demand of fundamentalists and chartists and the time-varying market shares of the two groups. It advances several different specifications of the endogenous switching between the trading strategies and then estimates these models by the method of simulated moments (MSM), where the choice of the moments reflects the basic stylized facts of the daily returns of a stock market index. In addition to the standard version of MSM with a quadratic loss function, we also take into account how often a great number of Monte Carlo simulation runs happen to yield moments that are all contained within their empirical confidence intervals. The model contest along these lines reveals a strong role for a (tamed) herding component. The quantitative performance of the winner model is so good that it may provide a standard for future research.JEL classification: D84; G12; G14; G15.

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Section: Resultsmentioning

confidence: 99%

Structural stochastic volatility in asset pricing dynamics: Estimation and model contest

Franke

Westerhoff

2012

Journal of Economic Dynamics and Control

197

186

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“…On the other hand, u n close to the right endpoint will result in inefficient estimates of j. Goldie and Smith (1987) and Smith (1987) derive the asymptotic distribution functions of both the maximum-likelihood and Hill estimators of the tail index for a class of distribution functions such that 1 À FðxÞ ¼ x À 1 j LðxÞ, where L(x) are slowly varying functions of different types. They also discuss in detail asymptotic bias and variance for these estimators and find that departures of F from a Pareto distribution function lead to biased and inefficient estimates of the tail index for both estimators.…”

Section: Pfm Nmentioning

confidence: 99%

Which Extreme Values Are Really Extreme?

Gonzalo

Olmo

2004

Journal of Financial Econometrics

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We define the extreme values of any random sample of size n from a distribution function F as the observations exceeding a threshold and following a type of generalized Pareto distribution (GPD) involving the tail index of F. The threshold is the order statistic that minimizes a Kolmogorov-Smirnov statistic between the empirical distribution of the corresponding largest observations and the corresponding GPD. To formalize the definition we use a semiparametric bootstrap to test the corresponding GPD approximation. Finally, we use our methodology to estimate the tail index and value at risk (VaR) of some financial indexes of major stock markets. keywords: bootstrap, extreme values, goodness-of-fit test, Hill estimator, Pickands theorem, VaRRisk management is one of the most important innovations of the 20th century in economics. During the last decade financial markets have realized the importance of monitoring risk. The question one would like to answer is: ''If things go wrong, how wrong can they go?'' The variance used as a risk measure is unable to answer this question.Alternative measures regarding possible values out of the range of available information need to be defined and calculated. Extreme value theory (EVT) provides the tools to model the asymptotic distribution of the maximum of a sequence of random variables {X n }, and in this sense this theory can be very helpful in order to obtain a first impression about how wrong things

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“…The "home bias" effects are also shown by Figure 3 where NB has more contribution to the crash probabilities of the five biggest Canadian banks than major international banks 10 .…”

Section: Measuring Systemic Importance Of Canadian Banksmentioning

confidence: 84%

“…A number of methods have been proposed to select k in finite samples. Goldie and Smith (1987) suggest to select the parameter k so as to minimize the asymptotic mean-squared error. In this paper, we use the heuristic procedure by the tail estimator as a function of k and select k in a region whereη is stable.…”

Section: Estimation Approachmentioning

confidence: 99%

Measuring systemic importance of financial institutions: An extreme value theory approach

Gravelle

2013

Journal of Banking & Finance

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In this paper, we define a financial institution's contribution to financial systemic risk as the increase in financial systemic risk conditional on the crash of the financial institution. The higher the contribution is, the more systemically important is the institution for the system. Based on relevant but different measurements of systemic risk, we propose a set of market-based measures on the systemic importance of financial institutions, each designed to capture certain aspects of systemic risk. Multivariate extreme value theory approach is used to estimate these measures. Using six big Canadian banks as the proxy for Canadian banking sector, we apply these measures to identify systemically important banks in Canadian banking sector and major risk contributors from international financial institutions to Canadian banking sector. The empirical evidence reveals that (i) the top three banks, RBC Financial Group, TD Bank Financial Group, and Scotiabank are more systemically important than other banks, although with different order from different measures, while we also find that the size of a financial institution should not be considered as a proxy of systemic importance; (ii) compared to the European and Asian banks, the crashes of U.S. banks, on average, are the most damaging to the Canadian banking sector, while the risk contribution to the Canadian banking sector from Asian banks is quite lower than that from banks in U.S. and euro area; (iii) the risk contribution to the Canadian banking sector exhibits " home bias ", that is, cross-country risk contribution tends to be smaller than domestic risk contribution. JEL classification: C14, C58, G21, G32 Bank classification: Financial stability; Financial system regulation and policies; Financial institutions; Econometric and statistical methods RésuméLes auteurs définissent la contribution d'une institution financière au risque systémique financier comme la hausse que connaîtrait ce risque si l'institution s'effondrait. Plus l'établissement en question contribue au risque systémique, plus il revêt de l'importance du point de vue du système. En se basant sur différentes mesures pertinentes de ce risque, les auteurs proposent un assortiment d'indicateurs de marché de l'importance systémique des institutions financières, dont chacun rend compte d'aspects distincts du risque systémique et qui sont construits à partir de techniques multivariées inspirées de la théorie des valeurs extrêmes. Armés de ces indicateurs, ils repèrent les institutions d'importance systémique dans le secteur bancaire canadien (ramené aux six principales banques du pays) ainsi que les institutions financières étrangères qui contribuent de façon significative au niveau de risque à l'échelle du secteur. Trois grandes conclusions ressortent de leurs estimations. D'abord, les trois plus grosses banques -RBC Groupe financier, le Groupe Financier Banque TD et la Banque Scotia -ont un poids systémique plus élevé, mais leur classement par ordre d'importance varie selon l'indicateur utilisé;...

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Slow Variation With Remainder: Theory and Applications

Cited by 186 publications

References 0 publications

Structural stochastic volatility in asset pricing dynamics: Estimation and model contest

Structural stochastic volatility in asset pricing dynamics: Estimation and model contest

Which Extreme Values Are Really Extreme?

Measuring systemic importance of financial institutions: An extreme value theory approach

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