12 research outputs found
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An extreme value theory approach to calculating minimum capital risk requirements
This paper investigates the frequency of extreme events for three LIFFE futures contracts for
the calculation of minimum capital risk requirements (MCRRs). We propose a semiparametric
approach where the tails are modelled by the Generalized Pareto Distribution and
smaller risks are captured by the empirical distribution function. We compare the capital
requirements form this approach with those calculated from the unconditional density and
from a conditional density - a GARCH(1,1) model. Our primary finding is that both in-sample
and for a hold-out sample, our extreme value approach yields superior results than either of
the other two models which do not explicitly model the tails of the return distribution. Since
the use of these internal models will be permitted under the EC-CAD II, they could be widely
adopted in the near future for determining capital adequacies. Hence, close scrutiny of
competing models is required to avoid a potentially costly misallocation capital resources
while at the same time ensuring the safety of the financial system
Numerical convergence of the block-maxima approach to the Generalized Extreme Value distribution
In this paper we perform an analytical and numerical study of Extreme Value
distributions in discrete dynamical systems. In this setting, recent works have
shown how to get a statistics of extremes in agreement with the classical
Extreme Value Theory. We pursue these investigations by giving analytical
expressions of Extreme Value distribution parameters for maps that have an
absolutely continuous invariant measure. We compare these analytical results
with numerical experiments in which we study the convergence to limiting
distributions using the so called block-maxima approach, pointing out in which
cases we obtain robust estimation of parameters. In regular maps for which
mixing properties do not hold, we show that the fitting procedure to the
classical Extreme Value Distribution fails, as expected. However, we obtain an
empirical distribution that can be explained starting from a different
observable function for which Nicolis et al. [2006] have found analytical
results.Comment: 34 pages, 7 figures; Journal of Statistical Physics 201
The non-random walk of stock prices: The long-term correlation between signs and sizes
We investigate the random walk of prices by developing a simple model
relating the properties of the signs and absolute values of individual price
changes to the diffusion rate (volatility) of prices at longer time scales. We
show that this benchmark model is unable to reproduce the diffusion properties
of real prices. Specifically, we find that for one hour intervals this model
consistently over-predicts the volatility of real price series by about 70%,
and that this effect becomes stronger as the length of the intervals increases.
By selectively shuffling some components of the data while preserving others we
are able to show that this discrepancy is caused by a subtle but long-range
non-contemporaneous correlation between the signs and sizes of individual
returns. We conjecture that this is related to the long-memory of transaction
signs and the need to enforce market efficiency.Comment: 9 pages, 5 figures, StatPhys2
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The effect of asymmetries on stock index return value-at-risk estimates
It is widely accepted that equity return volatility increases more following negative shocks rather than positive shocks. However, much of value-at-risk (VaR) analysis relies on the assumption that returns are normally distributed (a symmetric distribution). This article considers the effect of asymmetries on the evaluation and accuracy of VaR by comparing estimates based on various models
From value at risk to stress testing The extreme value approach
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