2,383 research outputs found
Continuous Equilibrium in Affine and Information-Based Capital Asset Pricing Models
We consider a class of generalized capital asset pricing models in continuous
time with a finite number of agents and tradable securities. The securities may
not be sufficient to span all sources of uncertainty. If the agents have
exponential utility functions and the individual endowments are spanned by the
securities, an equilibrium exists and the agents' optimal trading strategies
are constant. Affine processes, and the theory of information-based asset
pricing are used to model the endogenous asset price dynamics and the terminal
payoff. The derived semi-explicit pricing formulae are applied to numerically
analyze the impact of the agents' risk aversion on the implied volatility of
simultaneously-traded European-style options.Comment: 24 pages, 4 figure
Derivative pricing for a multi-curve extension of the Gaussian, exponentially quadratic short rate model
The recent financial crisis has led to so-called multi-curve models for the
term structure. Here we study a multi-curve extension of short rate models
where, in addition to the short rate itself, we introduce short rate spreads.
In particular, we consider a Gaussian factor model where the short rate and the
spreads are second order polynomials of Gaussian factor processes. This leads
to an exponentially quadratic model class that is less well known than the
exponentially affine class. In the latter class the factors enter linearly and
for positivity one considers square root factor processes. While the square
root factors in the affine class have more involved distributions, in the
quadratic class the factors remain Gaussian and this leads to various
advantages, in particular for derivative pricing. After some preliminaries on
martingale modeling in the multi-curve setup, we concentrate on pricing of
linear and optional derivatives. For linear derivatives, we exhibit an
adjustment factor that allows one to pass from pre-crisis single curve values
to the corresponding post-crisis multi-curve values
Moody's Correlated Binomial Default Distributions for Inhomogeneous Portfolios
This paper generalizes Moody's correlated binomial default distribution for
homogeneous (exchangeable) credit portfolio, which is introduced by Witt, to
the case of inhomogeneous portfolios. As inhomogeneous portfolios, we consider
two cases. In the first case, we treat a portfolio whose assets have uniform
default correlation and non-uniform default probabilities. We obtain the
default probability distribution and study the effect of the inhomogeneity on
it. The second case corresponds to a portfolio with inhomogeneous default
correlation. Assets are categorized in several different sectors and the
inter-sector and intra-sector correlations are not the same. We construct the
joint default probabilities and obtain the default probability distribution. We
show that as the number of assets in each sector decreases, inter-sector
correlation becomes more important than intra-sector correlation. We study the
maximum values of the inter-sector default correlation. Our generalization
method can be applied to any correlated binomial default distribution model
which has explicit relations to the conditional default probabilities or
conditional default correlations, e.g. Credit Risk, implied default
distributions. We also compare some popular CDO pricing models from the
viewpoint of the range of the implied tranche correlation.Comment: 29 pages, 17 figures and 1 tabl
Similarity thresholds used in DNA sequence assembly from short reads can reduce the comparability of population histories across species
Comparing inferences among datasets generated using short read sequencing may provide insight into the concerted impacts of divergence, gene flow and selection across organisms, but comparisons are complicated by biases introduced during dataset assembly. Sequence similarity thresholds allow the de novo assembly of short reads into clusters of alleles representing different loci, but the resulting datasets are sensitive to both the similarity threshold used and to the variation naturally present in the organism under study. Thresholds that require high sequence similarity among reads for assembly (stringent thresholds) as well as highly variable species may result in datasets in which divergent alleles are lost or divided into separate loci (‘over-splitting’), whereas liberal thresholds increase the risk of paralogous loci being combined into a single locus (‘under-splitting’). Comparisons among datasets or species are therefore potentially biased if different similarity thresholds are applied or if the species differ in levels of within-lineage genetic variation. We examine the impact of a range of similarity thresholds on assembly of empirical short read datasets from populations of four different non-model bird lineages (species or species pairs) with different levels of genetic divergence. We find that, in all species, stringent similarity thresholds result in fewer alleles per locus than more liberal thresholds, which appears to be the result of high levels of over-splitting. The frequency of putative under-splitting, conversely, is low at all thresholds. Inferred genetic distances between individuals, gene tree depths, and estimates of the ancestral mutation-scaled effective population size (θ) differ depending upon the similarity threshold applied. Relative differences in inferences across species differ even when the same threshold is applied, but may be dramatically different when datasets assembled under different thresholds are compared. These differences not only complicate comparisons across species, but also preclude the application of standard mutation rates for parameter calibration. We suggest some best practices for assembling short read data to maximize comparability, such as using more liberal thresholds and examining the impact of different thresholds on each dataset
Affine term structure models : a time-changed approach with perfect fit to market curves
We address the so-called calibration problem which consists of fitting in a
tractable way a given model to a specified term structure like, e.g., yield or
default probability curves. Time-homogeneous jump-diffusions like Vasicek or
Cox-Ingersoll-Ross (possibly coupled with compounded Poisson jumps, JCIR), are
tractable processes but have limited flexibility; they fail to replicate actual
market curves. The deterministic shift extension of the latter (Hull-White or
JCIR++) is a simple but yet efficient solution that is widely used by both
academics and practitioners. However, the shift approach is often not
appropriate when positivity is required, which is a common constraint when
dealing with credit spreads or default intensities. In this paper, we tackle
this problem by adopting a time change approach. On the top of providing an
elegant solution to the calibration problem under positivity constraint, our
model features additional interesting properties in terms of implied
volatilities. It is compared to the shift extension on various credit risk
applications such as credit default swap, credit default swaption and credit
valuation adjustment under wrong-way risk. The time change approach is able to
generate much larger volatility and covariance effects under the positivity
constraint. Our model offers an appealing alternative to the shift in such
cases.Comment: 44 pages, figures and table
Full Connectivity: Corners, edges and faces
We develop a cluster expansion for the probability of full connectivity of
high density random networks in confined geometries. In contrast to percolation
phenomena at lower densities, boundary effects, which have previously been
largely neglected, are not only relevant but dominant. We derive general
analytical formulas that show a persistence of universality in a different form
to percolation theory, and provide numerical confirmation. We also demonstrate
the simplicity of our approach in three simple but instructive examples and
discuss the practical benefits of its application to different models.Comment: 28 pages, 8 figure
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