McNeil, A. and Frey, R. (2000) Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: an Extrem Value Approach. Journal of Empirical Finance, 7: 271-300  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of the parameters of the GPD model since we would expect the high threshold u to be violated more often during periods of high volatility. Smith [Smi00] suggests using Bayesian techniques to model time varying GPD parameters. In this section, we review a model proposed by McNeil and Frey [MF00] which extends the EVT methodology to models of financial time series that allow for stochastic volatility and apply this model to the NASDAQ data set. 0.5 0 0.5 1 0 10 20 30 0.5 0 0.5 1 0 10 20 30 0.5 0 0.5 1 0 10 20 30 0.5 0 0.5 1 Figure 19: Sample auto correlation ....

A. McNeil and R. Frey. Estimation of tail-related risk measures for heteroscedastic financial time series: An extreme value approach. Journal of Empirical Finance, 7:271--300, 2000.

.... include Bouchaud, Sornette, and Potters [9] Danielsson and de Vries [12] Eberlein and Keller [15] Eberlein, Keller, and Prause [16] Embrechts, McNeil, and Straumann [18] Hosking, Bonti, and Siegel [26] Huisman, Koedijk, Kool, and Palm [27] Koedijk, Huisman, and Pownall [33] McNeil and Frey [40], Heyde [25] Using di#erent approaches to the problem and di#erent sets of data, these studies consistently find high kurtosis and heavy tails. Moreover, most studies find that the tails in financial data are not so heavy as to produce 2 infinite variance (as would be implied by a non normal ....

McNeil, A.J., and Frey, R. (1999) Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: an Extreme Value Approach, working paper, RiskLab, ETH Zurich.

....(1991) and Heston (1993) The key idea using stochastic volatility in risk management is to devolatilize the observed return series and to revolatilize with an appropriate forecast value. This idea has been applied in several recent papers (Hull and White (1998) Barone Adesi et al. 1998, 1999) McNeil and Frey (2001)) Since we have always a portfolio view any portfolio as complex as it may be is considered as a security of its own we study here a data set consisting of the daily closing DAX values from 1992 to 1999. The DAX represents a portfolio of 30 German blue chip stocks and reflects the behaviour ....

McNeil, A. and R. Frey (2001). Estimation of tail-related risk measures for heteroscedastic financial time series: An extreme value approach. Journal of Empirical Finance, forthcoming.

....variance, standardized skewness, standardized excess kurtosis, and the Jarque Bera test for normality. Table 1] 5 For a review of the different approaches to calculating VaR, see, for instance, Dowd (1998) or Jorion (2000) 6 For the use of extreme value theory with volatility updating see McNeill and Frey (2000). 9 As is commonly found for daily aggregate equity returns, normality is very strongly rejected, with all three series displaying significant excess kurtosis. There is also some evidence of skewness, although its interpretation in the presence of excess kurtosis is not straightforward (see ....

McNeil, A., and R. Frey, 2000, Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: An Extreme Value Approach , Journal Of Empirical Finance 7, 271-300.

.... estimate VaR, including the calculation of con dence intervals for VaR How to properly scale VaR, especially over (much) longer holding periods (a month to a year say) How to model VaR dynamically in a stochastic volatility or regime switching environment; see for instance McNeil and Frey [14] for a discussion on the former Give improved risk measures beyond VaR: a standard example being tail conditional VaR: E ( X j X VaR (X) 3) The latter measure yields a non trivial improvement on VaR for skew (typically non multivariate normal) risks. But independent from the ....

McNeil, A.J. and Frey, R. (1999) Estimation of tail{related risk measures for heteroscedastic nancial time series: an extreme value approach. J. Empir. Fin., to appear. ETH preprint. (www.math.ethz.ch/mcneil/pub list.html).

.... data to econometric time series models as for example vector auto regressive models with error correction (VECM) proposed by RiskMetrics [15] or generalized autoregressive conditionally heteroscedastic models (GARCH) Then we suggest some models based on Extreme Value Theory (McNeil and Frey [12], Dacorogna, Muller, Pictet and de Vries [5] In parallel, a study will be done about the normality assumption of low frequency data, in sight of using a version of the central limit theorem. Let s recall some useful definitions which will be the basis of our study. Definition 1.1 Let G be the ....

McNeil A.J. and Frey R. (1999) Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: an Extreme Value Approach, Preprint ETHZ. 34 Roger Kaufmann and Pierre Patie

....on this estimation procedure we cannot reject the hypothesis that the right and left tails are equally heavy. In the literature Student and generalised Pareto distributions, as heavy tailed distributions, were fitted to the residuals; see for example Baillie and Bollerslev [2] and McNeil and Frey [34]. As regards the tails of the distribution of Z, the choice of a Student distribution is certainly closer to reality than the assumption of normality. However, the tails of X and oe are determined by the center and the tails of the distribution of Z; see the discussion below. For this reason, in ....

McNeil, A.J. and Frey, R. (1998) Estimation of tail--related risk measures for heteroscedastic financial time series: an extreme value approach. Technical Report. Departement Mathematik, ETHZ Zurich.

....or hourly losses and pro ts from trading a particular instrument or group of instruments, the block maxima method provides a model which may be appropriate for the quarterly or annual maximum of such values. We see a possible role for this method in the de nition and analysis of stress losses (McNeil 1998) and will return to this subject in Section 4.1. A more modern group of models are the peaks over threshold (POT) models; these are models for all large observations which exceed a high threshold. The POT models are generally considered to be the most useful for practical applications, due to ....

....analyses suggest the conditional distribution of appropriate SV models for real data is often heavier tailed than the normal distribution. The trick as far as augmenting the dynamic procedure with EVT is concerned, is to apply it to the random variables Z t rather than X t . In the EVT approach (McNeil Frey 1998) we avoid assuming any particular form for F Z (z) instead we apply the GPD tail estimation procedure to this distribution. We assume that above some high threshold u the excess distribution is exactly GPD. The problem with the statistical estimation of this model is that the Z t variables ....

[Article contains additional citation context not shown here]

McNeil, A. & Frey, R. (1998), `Estimation of tail-related risk measures for heteroscedastic nancial time series: an extreme value approach', preprint, ETH Zurich.

....of weighted nonparametric regression. Much work in empirical nance suggests that GARCH type models with Gaussian innovations cannot capture the leptokurtosis and conditional heteroscedasticity of typical nancial return data. This work suggests that heavier tailed innovations are required; see McNeil and Frey (1999). It is thus attractive to look at exible tting methods such as our nonparametric GARCH algorithm that do not require us to x the form of the innovation distribution. Appendix Proof of Theorem 1. Write k 2 t;m 2 t k 2 t;n;m k 2 t;m 2 t;m k 2 k 2 t;m 2 t k 2 : ....

McNeil, A., and R. Frey (1999): \Estimation of tail-related risk measures for heteroscedastic nancial time series: an extreme value approach," preprint, ETH Zurich.

No context found.

McNeil, A. and Frey, R. (2000) Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: an Extrem Value Approach. Journal of Empirical Finance, 7: 271-300

No context found.

McNeil, A.J. & Frey, R. (1998). Estimation of tail-related risk measures for heteroscedastic nancial time series: an extreme value approach. Preprint, Dept. of Mathematics, ETH Zurich, Switzerland.

No context found.

McNeil, A.J. and Frey, R. (2000). Estimation of tail-related risk measures for heteroscedastic nancial time series: an extreme value approach. J. of Empirical Finance 7, 271-300.

No context found.

McNeil, A.J. and Frey, R. (2000). Estimation of tail-related risk measures for heteroscedastic nancial time series: an extreme value approach. J. of Empirical Finance 7, 271-300.

No context found.

McNeil, A.J. and Frey, R. (2000). Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: an Extreme Value Approach. Journal of Empirical Finance, 7, 271-300.

No context found.

McNeil, A.J. and Frey, R. (2000). Estimation of tail-related risk measures for heteroscedastic nancial time series: an extreme value approach. To appear in J. of Empirical Finance. 11

No context found.

McNeil, A.J. and Frey, R. (2000). Estimation of tail-related risk measures for heteroscedastic nancial time series: an extreme value approach. To appear in J. of Empirical Finance.

No context found.

McNeil, A.J. & Frey, R. (1998). Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach. Preprint, Dept. of Mathematics, ETH Zurich, Switzerland.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC