326 research outputs found
Approximating the numéraire portfolio by naive diversification
Estimation theory has shown, owing to the limited estimation window available for real asset data, that the sample-based Markowitz mean-variance approach produces unreliable weights that fluctuate substantially over time. This article proposes an alternate approach to portfolio optimization, being the use of naive diversification to approximate the numéraire portfolio (NP). The NP is the strictly positive portfolio that, when used as benchmark, makes all benchmarked non-negative portfolios either mean decreasing or trendless. Furthermore, it maximizes expected logarithmic utility and outperforms any other strictly positive portfolio in the long run. The article proves for a well-securitized market that the naive equal value-weighted portfolio converges to the NP when the number of constituents tends to infinity. This result is model independent and, therefore, very robust. The systematic construction of diversified stock indices by naive diversification from real data is demonstrated. Even when taking transaction costs into account, these indices significantly outperform the corresponding market capitalization- weighted indices in the long run, indicating empirically their asymptotic proximity to the NP. Finally, in the time of financial crisis, a large equi-weighted fund carrying the investments of major pension funds and insurance companies would provide important liquidity. It would not only dampen the drawdown of a crisis, but would also moderate the excesses of an asset price bubble. © 2012 Macmillan Publishers Ltd
Empirical behavior of a world stock index from intra-day to monthly time scales
Most of the papers that study the distributional and fractal properties of financial instruments focus on stock prices or foreign exchange rates. This typically leads to mixed results concerning the distributions of log-returns and some multi-fractal properties of exchange rates, stock prices, and regional indices. This paper uses a well diversified world stock index as the central object of analysis. Such index approximates the growth optimal portfolio, which is demonstrated under the benchmark approach, it is the ideal reference unit for studying basic securities. When denominating this world index in units of a given currency, one measures the movements of the currency against the entire market. This provides a least disturbed observation of the currency dynamics. In this manner, one can expect to disentangle, e.g., the superposition of the two currencies involved in an exchange rate. This benchmark approach to the empirical analysis of financial data allows us to establish remarkable stylized facts. Most important is the observation that the repeatedly documented multi-fractal appearance of financial time series is very weak and much less pronounced than the deviation of the mono-scaling properties from Brownian-motion type scaling. The generalized Hurst exponent H(2) assumes typical values between 0.55 and 0.6. Accordingly, autocorrelations of log-returns decay according to a power law, and the quadratic variation vanishes when going to vanishing observation time step size. Furthermore, one can identify the Studentt distribution as the log-return distribution of a well-diversified world stock index for long time horizons when a long enough data series is used for estimation. The study of dependence properties, finally, reveals that jumps at daily horizon originate primarily in the stock market while at 5min horizon they originate in the foreign exchange market. The principal message of the empirical analysis is that there is evidence that a diffusion model without multi-scaling could reasonably well model the dynamics of a broadly diversified world stock inde
Recursive marginal quantization of higher-order schemes
© 2018 Informa UK Limited, trading as Taylor & Francis Group. Quantization techniques have been applied in many challenging finance applications, including pricing claims with path dependence and early exercise features, stochastic optimal control, filtering problems and efficient calibration of large derivative books. Recursive marginal quantization (RMQ) of the Euler scheme has recently been proposed as an efficient numerical method for evaluating functionals of solutions of stochastic differential equations. This method involves recursively quantizing the conditional marginals of the discrete-time Euler approximation of the underlying process. By generalizing this approach, we show that it is possible to perform RMQ for two higher-order schemes: the Milstein scheme and a simplified weak order 2.0 scheme. We further extend the applicability of RMQ by showing how absorption and reflection at the zero boundary may be incorporated, when necessary. To illustrate the improved accuracy of the higher-order schemes, various computations are performed using geometric Brownian motion and the constant elasticity of variance model. For both models, we provide evidence of improved weak order convergence and computational efficiency. By pricing European, Bermudan and barrier options, further evidence of improved accuracy of the higher-order schemes is demonstrated
On the rate of convergence of simple and jump-adapted weak Euler schemes for Levy driven SDEs
The paper studies the rate of convergence of the weak Euler approximation for
solutions to possibly completely degenerate SDEs driven by Levy processes, with
Hoelder-continuous coefficients. It investigates the dependence of the rate on
the regularity of coefficients and driving processes. In addition, the rate
robustness to the approximation of the increments of the driving process is
studied and approximate Euler scheme considered. A rate of convergence is
derived for an approximate jump-adapted scheme as well.Comment: A part on approximate jump adapted Euler scheme adde
Memorandum on a new financial architecture and new regulations
The financial crisis is global and is deeply rooted in a decade-long misuse of the financial market for rent-seeking. The financial industry has largely abandoned its role as a service industry, supposedly charging reasonable fees for the services of spreading risk and allocating capital and credit. Instead it provides a market for corporate control –mergers and acquisitions– and a casino for betting on or hedging practically any kind of risk –the derivatives market–.Publisher's Versio
Alignments of Voids in the Cosmic Web
We investigate the shapes and mutual alignment of voids in the large scale
matter distribution of a LCDM cosmology simulation. The voids are identified
using the novel WVF void finder technique. The identified voids are quite
nonspherical and slightly prolate, with axis ratios in the order of c:b:a
approx. 0.5:0.7:1. Their orientations are strongly correlated with significant
alignments spanning scales >30 Mpc/h.
We also find an intimate link between the cosmic tidal field and the void
orientations. Over a very wide range of scales we find a coherent and strong
alignment of the voids with the tidal field computed from the smoothed density
distribution. This orientation-tide alignment remains significant on scales
exceeding twice the typical void size, which shows that the long range external
field is responsible for the alignment of the voids. This confirms the view
that the large scale tidal force field is the main agent for the large scale
spatial organization of the Cosmic Web.Comment: 10 pages, 4 figures, submitted to MNRAS, for high resolution version,
see http://www.astro.rug.nl/~weygaert/tim1publication/voidshape.pd
Unfolding the Hierarchy of Voids
We present a framework for the hierarchical identification and
characterization of voids based on the Watershed Void Finder. The Hierarchical
Void Finder is based on a generalization of the scale space of a density field
invoked in order to trace the hierarchical nature and structure of cosmological
voids. At each level of the hierarchy, the watershed transform is used to
identify the voids at that particular scale. By identifying the overlapping
regions between watershed basins in adjacent levels, the hierarchical void tree
is constructed. Applications on a hierarchical Voronoi model and on a set of
cosmological simulations illustrate its potential.Comment: 5 pages, 2 figure
Cavity evolution in relativistic self-gravitating fluids
We consider the evolution of cavities within spherically symmetric
relativistic fluids, under the assumption that proper radial distance between
neighboring fluid elements remains constant during their evolution (purely
areal evolution condition). The general formalism is deployed and solutions are
presented. Some of them satisfy Darmois conditions whereas others present
shells and must satisfy Israel conditions, on either one or both boundary
surfaces. Prospective applications of these results to some astrophysical
scenarios is suggested.Comment: 10 pages Revtex. To appear in Class. Quantum Grav
The Void Galaxy Survey: Optical Properties and H I Morphology and Kinematics
We have carefully selected a sample of 60 galaxies that reside in the deepest
underdensities of geometrically identified voids within the SDSS. HI imaging of
55 galaxies with the WSRT reveals morphological and kinematic signatures of
ongoing interactions and gas accretion. We probe a total volume of 485 Mpc^3
within the voids, with an angular resolution of 8 kpc at an average distance of
85 Mpc. We reach column density sensitivities of 5 x 10^19 cm^-2, corresponding
to an HI mass limit of 3 x 10^8 M_sun. We detect HI in 41 galaxies, with total
masses ranging from 1.7 x 10^8 to 5.5 x 10^9 M_sun. The upper limits on the 14
non-detections are not inconsistent with their luminosities, given their
expected HI mass to light ratios. We find that the void galaxies are generally
gas rich, low luminosity, blue disk galaxies, with optical and HI properties
that are not unusual for their luminosity and morphology. The sample spans a
range of absolute magnitudes (-16.1 > M_r > -20.4) and colors (0.06 < g-r <
0.87), and includes disk and irregular galaxies. We also identify three as
early type galaxies, all of which are not detected in HI. All galaxies have
stellar masses less than 3 x 10^10 M_sun, and many have kinematic and
morphological signs of ongoing gas accretion, suggesting that the void galaxy
population is still in the process of assembling. The small scale clustering in
the void, within 600 kpc and 200 km/s, is similar to that in higher density
regions, and we identify 18 HI rich neighboring galaxies in the voids. Most are
within 100 kpc and 100 km/s of the targeted galaxy, and we find no significant
population of HI rich low luminosity galaxies filling the voids, contrary to
what is predicted by simulations.Comment: 34 pages, 33 figures (including Atlas in Appendix), accepted for
publication in A
Only the Lonely: H I Imaging of Void Galaxies
Void galaxies, residing within the deepest underdensities of the Cosmic Web,
present an ideal population for the study of galaxy formation and evolution in
an environment undisturbed by the complex processes modifying galaxies in
clusters and groups, as well as provide an observational test for theories of
cosmological structure formation. We have completed a pilot survey for the HI
imaging aspects of a new Void Galaxy Survey (VGS), imaging 15 void galaxies in
HI in local (d < 100 Mpc) voids. HI masses range from 3.5 x 10^8 to 3.8 x 10^9
M_sun, with one nondetection with an upper limit of 2.1 x 10^8 M_sun. Our
galaxies were selected using a structural and geometric technique to produce a
sample that is purely environmentally selected and uniformly represents the
void galaxy population. In addition, we use a powerful new backend of the
Westerbork Synthesis Radio Telescope that allows us to probe a large volume
around each targeted galaxy, simultaneously providing an environmentally
constrained sample of fore- and background control sample of galaxies while
still resolving individual galaxy kinematics and detecting faint companions in
HI. This small sample makes up a surprisingly interesting collection of
perturbed and interacting galaxies, all with small stellar disks. Four galaxies
have significantly perturbed HI disks, five have previously unidentified
companions at distances ranging from 50 to 200 kpc, two are in interacting
systems, and one was found to have a polar HI disk. Our initial findings
suggest void galaxies are a gas-rich, dynamic population which present evidence
of ongoing gas accretion, major and minor interactions, and filamentary
alignment despite the surrounding underdense environment.Comment: 53 pages, 18 figures, accepted for publication in AJ. High resolution
available at http://www.astro.columbia.edu/~keejo/kreckel2010.pd
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