A Cosmic Watershed: the WVF Void Detection Technique

On megaparsec scales the Universe is permeated by an intricate filigree of clusters, filaments, sheets and voids, the Cosmic Web. For the understanding of its dynamical and hierarchical history it is crucial to identify objectively its complex morphological components. One of the most characteristic aspects is that of the dominant underdense Voids, the product of a hierarchical process driven by the collapse of minor voids in addition to the merging of large ones. In this study we present an objective void finder technique which involves a minimum of assumptions about the scale, structure and shape of voids. Our void finding method, the Watershed Void Finder (WVF), is based upon the Watershed Transform, a well-known technique for the segmentation of images. Importantly, the technique has the potential to trace the existing manifestations of a void hierarchy. The basic watershed transform is augmented by a variety of correction procedures to remove spurious structure resulting from sampling noise. This study contains a detailed description of the WVF. We demonstrate how it is able to trace and identify, relatively parameter free, voids and their surrounding (filamentary and planar) boundaries. We test the technique on a set of Kinematic Voronoi models, heuristic spatial models for a cellular distribution of matter. Comparison of the WVF segmentations of low noise and high noise Voronoi models with the quantitatively known spatial characteristics of the intrinsic Voronoi tessellation shows that the size and shape of the voids are succesfully retrieved. WVF manages to even reproduce the full void size distribution function.Comment: 24 pages, 15 figures, MNRAS accepted, for full resolution, see http://www.astro.rug.nl/~weygaert/tim1publication/watershed.pd

Credit Derivative Evaluation and CVA Under the Benchmark Approach

© 2015, Springer Japan. In this paper, we discuss how to model credit risk under the benchmark approach. Firstly we introduce an affine credit risk model. We then show how to price credit default swaps (CDSs) and introduce credit valuation adjustment (CVA) as an extension of CDSs. In particular, our model can capture right-way—and wrong-way exposure. This means, we capture the dependence structure of the default event and the value of the transaction under consideration. For simple contracts, we provide closed-form solutions. However, due to the fact that we allow for a dependence between the default event and the value of the transaction, closed-form solutions are difficult to obtain in general. Hence we conclude this paper with a reduced form model, which is more tractable

Electronic and geometric structure of NH₃ on Ge(001) under equilibrium adsorption conditions

The adsorption of NH3 on the Ge(001) surface is studied by angle-resolved UV-photoelectron spectroscopy using synchrotron radiation and by high-resolution low-energy electron diffraction (LEED) measurements. On the clean surface, the phase transition from 2×1 to c(4×2) is observed over a temperature range from 400 to 220 K. Measurements during NH3 admission at varying temperature in adsorption-desorption equilibrium yield a sequential occupation of several states. Up to 1/2 ML (one molecule per reconstruction dimer), NH3 is bound strongly on the dimer down atoms with the Ge-N axis perpendicular to the surface (α state). The adsorption occurs via a mobile precursor state. The α state is connected with a (2×2) superstructure. Yet, the transition c(4×2)→(2×2) starts already at very low coverages (0.01 ML) and is completed for about 0.04 ML. We propose that a long-range attractive interaction causes α-NH3-island formation and that a short-range repulsive interaction is responsible for a change to 2×2 within the islands by a dimer flip of every second dimer row. At the island edges, this dimer flip continues over the clean part of the surface thus changing its structure to 2×2 long before 1/2 ML saturation. Beyond 1/2 ML, the structure changes again. A good-quality 2×1 structure is seen up to 4 ML indicating pseudomorphic growth up to this coverage. Beyond 4 ML, the adsorbate structure changes irreversibly to NH3-ice without any LEED pattern

A tractable model for indices approximating the growth optimal portfolio

The growth optimal portfolio (GOP) plays an important role in finance, where it serves as the numéraire portfolio, with respect to which contingent claims can be priced under the real world probability measure. This paper models the GOP using a time dependent constant elasticity of variance (TCEV) model. The TCEV model has high tractability for a range of derivative prices and fits well the dynamics of a global diversified world equity index. This is confirmed when pricing and hedging various derivatives using this index

THE NUMÉRAIRE PROPERTY AND LONG-TERM GROWTH OPTIMALITY FOR DRAWDOWN-CONSTRAINED INVESTMENTS

© 2014 Wiley Periodicals, Inc. We consider the portfolio choice problem for a long-run investor in a general continuous semimartingale model. We combine the decision criterion of pathwise growth optimality with a flexible specification of attitude toward risk, encoded by a linear drawdown constraint imposed on admissible wealth processes. We define the constrained numéraire property through the notion of expected relative return and prove that drawdown-constrained numéraire portfolio exists and is unique, but may depend on the investment horizon. However, when sampled at the times of its maximum and asymptotically as the time-horizon becomes distant, the drawdown-constrained numéraire portfolio is given explicitly through a model-independent transformation of the unconstrained numéraire portfolio. The asymptotically growth-optimal strategy is obtained as limit of numéraire strategies on finite horizons

A Hybrid Model for Pricing and Hedging of Long-dated Bonds

© 2015 Taylor & Francis. Abstract: Long-dated fixed income securities play an important role in asset-liability management, in life insurance and in annuity businesses. This paper applies the benchmark approach, where the growth optimal portfolio (GOP) is employed as numéraire together with the real-world probability measure for pricing and hedging of long-dated bonds. It employs a time-dependent constant elasticity of variance model for the discounted GOP and takes stochastic interest rate risk into account. This results in a hybrid framework that models the stochastic dynamics of the GOP and the short rate simultaneously. We estimate and compare a variety of continuous-time models for short-term interest rates using non-parametric kernel-based estimation. The hybrid models remain highly tractable and fit reasonably well the observed dynamics of proxies of the GOP and interest rates. Our results involve closed-form expressions for bond prices and hedge ratios. Across all models under consideration we find that the hybrid model with the 3/2 dynamics for the interest rate provides the best fit to the data with respect to lowest prices and least expensive hedges

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

A compact ultrahigh-vacuum system for the in situ investigation of III/V semiconductor surfaces

A compact ultrahigh vacuum (UHV) system has been built to study growth and properties of III/V semiconductor surfaces and nanostructures. The system allows one to grow III/V semiconductor surfaces by molecular beam epitaxy (MBE) and analyze their surface by a variety of surface analysis techniques. The geometric structure is examined by scanning tunneling microscopy (STM), low-energy electron diffraction and reflection high-energy electron diffraction. The electronic properties of the surfaces are studied by angular resolved photoemission either in the laboratory using a helium discharge lamp or at the Berlin Synchrotron Radiation Facility BESSY. In order to meet the space restriction at BESSY the system dimensions are kept very small. A detailed description of the apparatus and the sample handling system is given. For the UHV-STM (Park Scientific Instruments, VP2) a new, versatile tip handling mechanism has been developed. It allows the transfer of tips out of the chamber and furthermore, the in situ tip cleaning by electron annealing. In addition, another more reliable in situ tip-preparation technique operating the STM in the field emission regime is described. The ability of the system is shown by an atomically resolved STM image of the c(4×4) reconstructed GaAs(001) surface

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

Pricing currency derivatives under the benchmark approach

© 2014 Elsevier B.V. This paper considers the realistic modelling of derivative contracts on exchange rates. We propose a stochastic volatility model that recovers not only the typically observed implied volatility smiles and skews for short dated vanilla foreign exchange options but allows one also to price payoffs in foreign currencies, lower than possible under classical risk neutral pricing, in particular, for long dated derivatives. The main reason for this important feature is the strict supermartingale property of benchmarked savings accounts under the real world probability measure, which the calibrated parameters identify under the proposed model. Using a real dataset on vanilla option quotes, we calibrate our model on a triangle of currencies and find that the risk neutral approach fails for the calibrated model, while the benchmark approach still works