49,233 research outputs found
Mode-Seeking on Hypergraphs for Robust Geometric Model Fitting
In this paper, we propose a novel geometric model fitting method, called
Mode-Seeking on Hypergraphs (MSH),to deal with multi-structure data even in the
presence of severe outliers. The proposed method formulates geometric model
fitting as a mode seeking problem on a hypergraph in which vertices represent
model hypotheses and hyperedges denote data points. MSH intuitively detects
model instances by a simple and effective mode seeking algorithm. In addition
to the mode seeking algorithm, MSH includes a similarity measure between
vertices on the hypergraph and a weight-aware sampling technique. The proposed
method not only alleviates sensitivity to the data distribution, but also is
scalable to large scale problems. Experimental results further demonstrate that
the proposed method has significant superiority over the state-of-the-art
fitting methods on both synthetic data and real images.Comment: Proceedings of the IEEE International Conference on Computer Vision,
pp. 2902-2910, 201
Option-implied information and predictability of extreme returns : [Version 28 Januar 2013]
We study whether prices of traded options contain information about future extreme market events. Our option-implied conditional expectation of market loss due to tail events, or tail loss measure, predicts future market returns, magnitude, and probability of the market crashes, beyond and above other option-implied variables. Stock-specific tail loss measure predicts individual expected returns and magnitude of realized stock-specific crashes in the cross-section of stocks. An investor that cares about the left tail of her wealth distribution benefits from using the tail loss measure as an information variable to construct managed portfolios of a risk-free asset and market index
Modelling the Dynamic Relationship between Systematic Default and Recovery Risk
Default correlation modelling is becoming the most popular problem in the
field of credit derivatives pricing. An increase in default risk would cause the
recovery rate to change correspondingly. Correlation between default and
recovery rates has a noticeable effect on risk measures and credit derivatives
pricing.
After an introduction, we review the most recent literature covering default
correlation and the relationship between default and recovery rates. We
adopt the copula methodology to focus on estimating the default correlations
rather than focus on modelling probabilities of default, we then use stress
testing to compare the distributions of the probability of default under different
copula functions. We develop a Gamma-Beta model to link the recovery
rate directly with the individual probability of default, this is instead of an
extended one factor model to relate them by a systematic common factor.
One factor models are re-examined to explore correlated recovery rates under
three distributions: the Logit-normal, the Normal and the Log-normal. By
analyzing the results respectively obtained from these two classes of modelling
scheme, we argue that the direct dependence (Gamma-Beta) model
behaves better, in estimating the recovery rate given individual probability
of default and in suggesting a better indication of their relationship. Finally,
we apply default correlation and the correlated recovery rate to portfolio risk
modelling. We conclude that if the recovery rates are independent stochastic
variables, the expected losses in a large portfolio might be underestimated
because the uncorrelated recovery risks can be diversified, so the correlation
between default rate and recovery risk can not be neglected in the applications.
Here, we believe the first time, the recovery rate depends on individual
default probability by means of a closed formula
Maximum Entropy, Word-Frequency, Chinese Characters, and Multiple Meanings
The word-frequency distribution of a text written by an author is well
accounted for by a maximum entropy distribution, the RGF (random group
formation)-prediction. The RGF-distribution is completely determined by the a
priori values of the total number of words in the text (M), the number of
distinct words (N) and the number of repetitions of the most common word
(k_max). It is here shown that this maximum entropy prediction also describes a
text written in Chinese characters. In particular it is shown that although the
same Chinese text written in words and Chinese characters have quite
differently shaped distributions, they are nevertheless both well predicted by
their respective three a priori characteristic values. It is pointed out that
this is analogous to the change in the shape of the distribution when
translating a given text to another language. Another consequence of the
RGF-prediction is that taking a part of a long text will change the input
parameters (M, N, k_max) and consequently also the shape of the frequency
distribution. This is explicitly confirmed for texts written in Chinese
characters. Since the RGF-prediction has no system-specific information beyond
the three a priori values (M, N, k_max), any specific language characteristic
has to be sought in systematic deviations from the RGF-prediction and the
measured frequencies. One such systematic deviation is identified and, through
a statistical information theoretical argument and an extended RGF-model, it is
proposed that this deviation is caused by multiple meanings of Chinese
characters. The effect is stronger for Chinese characters than for Chinese
words. The relation between Zipf's law, the Simon-model for texts and the
present results are discussed.Comment: 15 pages, 10 figures, 2 table
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