5 research outputs found
Value-at-Risk time scaling for long-term risk estimation
In this paper we discuss a general methodology to compute the market risk
measure over long time horizons and at extreme percentiles, which are the
typical conditions needed for estimating Economic Capital. The proposed
approach extends the usual market-risk measure, ie, Value-at-Risk (VaR) at a
short-term horizon and 99% confidence level, by properly applying a scaling on
the short-term Profit-and-Loss (P&L) distribution. Besides the standard
square-root-of-time scaling, based on normality assumptions, we consider two
leptokurtic probability density function classes for fitting empirical P&L
datasets and derive accurately their scaling behaviour in light of the Central
Limit Theorem, interpreting time scaling as a convolution problem. Our analyses
result in a range of possible VaR-scaling approaches depending on the
distribution providing the best fit to empirical data, the desired percentile
level and the time horizon of the Economic Capital calculation. After assessing
the different approaches on a test equity trading portfolio, it emerges that
the choice of the VaR-scaling approach can affect substantially the Economic
Capital calculation. In particular, the use of a convolution-based approach
could lead to significantly larger risk measures (by up to a factor of four)
than those calculated using Normal assumptions on the P&L distribution.Comment: Pre-Print version, submitted to The Journal of Risk. 18 pages, 17
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Fractal fluctuations in quantum integrable scattering
We theoretically and numerically demonstrate that completely integrable
scattering processes may exhibit fractal transmission fluctuations, due to
typical spectral properties of integrable systems.
Similar properties also occur with scattering processes in the presence of
strong dynamical localization, thus explaining recent numerical observations of
fractality in the latter class of systems.Comment: revtex, 4 pages, 3 eps figure
Quantum Fractal Fluctuations
We numerically analyse quantum survival probability fluctuations in an open,
classically chaotic system. In a quasi-classical regime, and in the presence of
classical mixed phase space, such fluctuations are believed to exhibit a
fractal pattern, on the grounds of semiclassical arguments. In contrast, we
work in a classical regime of complete chaoticity, and in a deep quantum regime
of strong localization. We provide evidence that fluctuations are still
fractal, due to the slow, purely quantum algebraic decay in time produced by
dynamical localization. Such findings considerably enlarge the scope of the
existing theory.Comment: revtex, 4 pages, 5 figure