J. Danielsson and C. de Vries. Value at risk and extreme returns. In P. Embrechts, editor, Extremes and Integrated Risk Management, pages 85--106. Risk Books, 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....preset threshold. This is referred to as peaks over threshold (POT) modelling. We will discuss two approaches to POT modelling currently found in the literature. The first is a semi parametric approach based on a Hill type estimator of the tail index ( BTV96] Danielsson and de Vries [DdV97] and [DdV00], and Mills [Mil99] The second approach is a fully parametric approach based on the generalized Pareto distribution ( EKM97] McNeil [MS97] and Embrechts, Resnick and Samorodnitsky [ERS99] 6.4.1 Semiparametric Approach Recall that FX is in the maximum domain of attraction of the Frechet ....

J. Danielsson and C. de Vries. Value at risk and extreme returns. In P. Embrechts, editor, Extremes and Integrated Risk Management, pages 85--106. Risk Books, 2000.

....computation of the VaR for a collection of returns thus requires the computation of the empirical quantile at level # of the distribution of the returns of the portfolio. Most models in the literature focus on the computation of the VaR for negative returns (see van den Goorbergh and Vlaar, 1999; Danielsson and de Vries, 2000; Jorion, 2000) Indeed, it is assumed that traders or portfolio managers have long trading positions, i.e. they bought the traded asset and are concerned when the price of the asset falls. In this paper we focus on modelling VaR for portfolios defined on long and short trading positions. Thus we ....

Danielsson, J., and C. de Vries (2000): "Value-at-Risk and extreme returns," Annales d'Economie et Statistique, 3, 73--85.

....characteristic in line with futures returns. Whilst, futures returns may not exactly fit the Frecht distribution, this problem is overcome by measuring the tail values with the semi parametric Hill index. Previous applications of extreme value theory in risk management include Longin, 1999a; Danielsson and de Vries, 1997; and McNeil and Frey, 1998; where they outline extreme value theory assuming that asset price changes are identical and independently distributed (iid) However, the empirical evidence in the finance literature (Taylor, 1986; Ding and Granger, 1993; and Ding and Granger, 1996) provides contrary ....

....I (Gumbell) lim n [1 F(a n r b n ) e r t Type II (Frecht) lim 1 F(tr) r a = r (1 g) t 1 F(t) For r 0, a 0. Type III (Weibull) lim 1 F(tr u) r a = r (1 g) 4) t 1 F(t u) For r 0, a 0. 7 A vast literature on financial returns (Cotter, 1998; Danielsson and DeVries, 1997; Kearns and Pagan, 1997; Koedijk and Kool, 1992; and Venkataraman, 1997) and on derivative first differences (Cotter and McKillop, 2000; Duffie and Pan, 1997; Hull and White, 1998; and Longin, 1999b) has recognised the existence of fat tailed characteristics. For this reason the rest of the ....

Danielsson, J. & de Vries, C. G. (1997). Value at Risk and Extreme Returns, London School of Economics, Financial Markets Group Discussion Paper, No. 273.

....amount of capital required for each (netted) securities position to cover all but a small proportion of potential losses (typically 5.00 ) The sum of these positions is the firm s value at risk relating to its trading exposures. The standard value at risk methodology (for a critical appraisal see Danielsson and DeVries (1997), or Neftci (1998) requires that the underlying return generating distribution for the security in question is normally distributed, with moments which can be estimated using past data and do not time vary. The requirement that the underlying return generating process is normal and predictable ....

Danielsson, J. and C.G. De Vries, 1997, Value-at-Risk and Extreme Returns, LSE Working Paper Presented at the Issues of Empirical Finance (Financial Market Group), Nov 1997.

....complication, as it would render the model intractable. Time dependence is, however, a crucial component for a practical evaluation of VaR measures, see Christo#ersen #1998# for some possible methods. See also Christo#ersen and Diebold #1997#, Christo#ersen, Diebold, and Schuermann #1998#, and Danielsson and de Vries #1997# for further critical remarks on the #un#importance of time dependence for VaR calculations. The scalar in#ation factor f#t# used for transforming the VaR into a capital requirement is one of the crucial variables in this paper. It allows the supervisor to impose monetary penalties on banks with ....

Danielsson, J., and C.G. de Vries #1997#: #Value at Risk and Extreme Returns," Research Memorandum, University of Iceland.

....parametric distributions that capture all salient features of a credit loss distribution for large portfolios. Moreover, it may also be very di#cult to employ #semi nonparametric# extreme value statistical theory for estimating higher order quantiles of the credit loss distribution, see, e.g. Danielsson and Vries #1997#. Such methods presume a certain degree of homogeneity of tail observations, which might be inappropriate given the strongly varying tail behavior of C over di#erent parts of the portfolio. Deriving the tail behavior of credit losses for multi factor models is somewhat more complicated. We only ....

Danielsson, J. and C. D. Vries #1997#. Value-at-risk and extreme returns. mimeo.

....is appropriate for the calculation of large loss forecasts. Furthermore, even if the time horizon is shorter, financial institutions often prefer unconditional risk forecast methods to avoid undesirable frequent changes in risk limits for traders and portfolio managers. For more in this issue, see Danielsson (2000). For a typical large portfolio (in terms of number of assets) the conditional approach mayalso just not be feasible since this requires constructing and updating huge conditional variance covariance matrices. 3 2.1.2Condi3 55P Models Building on the realization that returns exhibit ....

....one has hit a high volatilityregime. Per contrast, GARCH performs better in signalling the continuation of a high risk regime since it adapts to the new situation. The conditional GARCH methodologythus necessarilyimplies more volatile risk forecasts then the unconditional approach; see e.g. Danielsson (2000) who find that risk volatilityfrom a GARCH model can be 4 times higher than for an unconditional model. Because the GARCH methodologyquickly adapts to recent market developments, it meets the VaR constraint more frequentlythan the unconditional approach. But this frequencyis just one aspect, the ....

Danielsson, J., and C. G. de Vries (1997c): "Value at Risk and Extreme Returns,"L ondon School of Economics, Financial Markets Group Discussion Paper, no. 273.

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Danielsson, J. and de Vries, C.G. (1998). Value-at-Risk and extreme returns. Mimeo.

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