Clustering of financial time series

This paper addresses the topic of classifying financial time series in a fuzzy framework proposing two fuzzy clustering models both based on GARCH models. In general clustering of financial time series, due to their peculiar features, needs the definition of suitable distance measures. At this aim, the first fuzzy clustering model exploits the autoregressive representation of GARCH models and employs, in the framework of a partitioning around medoids algorithm, the classical autoregressive metric. The second fuzzy clustering model, also based on partitioning around medoids algorithm, uses the Caiado distance, a Mahalanobis-like distance, based on estimated GARCH parameters and covariances that takes into account the information about the volatility structure of time series. In order to illustrate the merits of the proposed fuzzy approaches an application to the problem of classifying 29 time series of Euro exchange rates against international currencies is presented and discussed, also comparing the fuzzy models with their crisp version.     

Originalarbeiten 133m Xe zur Markierung von Gasphasen bei technischen Tracerexperimenten

Bei technischen Tracerexperimenten bereitet die Markierung von Gasphasen Schwierigkeiten, wenn man auf Außenwandmessungen angewiesen ist, da die Auswahl an geeigneten Radionukliden bzw. radioaktiv markierten Verbindungen dann sehr beschrānkt ist. Eine gute Ergänzung des Radionuklidangebotes für den genannten Zweck bietet ^133mXe, Halbwertszeit 2,3 d, E_γ = 0,23 MeV (16%). ^133mXe erhält man mit guten Ausbeuten bei einer Reaktoraktivierung von natürlichem Xenon. Die Sälligungsaktivität fär ^133mXe beträgt bei einem Fluß von 5,0 μ 10¹³ n/cm²s 48,5 mCi/cm³ Xenon (unter Normalbedingungen). An Veweilzeitmessungen von Gasphasen in technischen Anlagen werden die Einsatzmöglichkeiten des ^133mXe dargestellt.     

Assessment of health risk associated with natural gamma dose rate levels and isodose mapping of Jordan

ABSTRACT

As a pioneering study in Jordan, an extensive measurement for external gamma dose rate (GDR) was conducted. A portable gamma radiation detector was used to perform these measurements at 1?m above the soil surface. A geographical positioning system Garmin was used to record a total of 823 measured points. The GDRs’ measurement ranged from 35 to 470?nGy?h^?1 giving a mean value of 90?nGy?h^?1, which was found to be one and half times higher than the world average of 59?nGy?h^?1. The lowest mean GDR 72?nGy?h^?1 was found in the Albalqa governate, while the highest mean GDR 131?nGy?h^?1 was found to be for the Alkarak governate. The mean annual effective dose was found to be 0.551?mSv, which is higher than the world average value of 0.48?mSv. This is a pivotal study evaluating the risks associated with GDR levels in Jordan that were the relative excess lifetime cancer risk, the mean collective effective dose, the mean weighted GDR and the mean lifetime dose that are 2.24?×?10^?3, 5538manSv?y^?1, 0.531?mSv and 39?mSv, respectively. The cosmic rays mean GDR was determined to be 20?nGy?h^?1. This study focuses on constructing GDRs’ baseline data in Jordan, which will be used to determine the possible change in the natural radiation due to other human activities in the future. ArcGIS software was employed to generate an isodose map to characterise exposure rates caused by GDR in Jordan.     

Solving nonlinear inverse problems by evolution equations based on Gauss–Newton methods

In this article, we solve nonlinear inverse problems by an evolution equation method which can be viewed as the continuous analogue of the Gauss–Newton method. Under certain conditions we prove the convergence and derive the rate of convergence when the discrepancy principle is coupled.     

Local energy decay for the wave equation with a nonlinear time-dependent damping

This article addresses a wave equation on a exterior domain in ? ^d (d odd) with nonlinear time-dependent dissipation. Under a microlocal geometric condition we prove that the decay rates of the local energy functional are obtained by solving a nonlinear non-autonomous differential equation     

General decay for a porous thermoelastic system with a memory

In this paper, we consider a linear damped porous thermoelastic system of memory type where the heat conduction is given by Cattaneo’s Law . We establish a general decay results using an appropriate Lyapunov functional.     

Far Casting Cross-Validation

Cross-validation has long been used for choosing tuning parameters and other model selection tasks. It generally performs well provided the data are independent, or nearly so. Improvements have been suggested which address ordinary cross-validation’s (OCV) shortcomings in correlated data. Whereas these techniques have merit, they can still lead to poor model selection in correlated data or are not readily generalizable to high-dimensional data.

The proposed solution, far casting cross-validation (FCCV), addresses these problems. FCCV withholds correlated neighbors in every aspect of the cross-validation procedure. The result is a technique that stresses a fitted model’s ability to extrapolate rather than interpolate. This generally leads to better model selection in correlated datasets.

Whereas FCCV is less than optimal in the independence case, our improvement of OCV applies more generally to higher dimensional error processes and to both parametric and nonparametric model selection problems. To facilitate introduction, we consider only one application, namely estimating global bandwidths for curve estimation with local linear regression. We provide theoretical motivation and report some comparative results from a simulation experiment and on a time series of annual global temperature deviations. For such data, FCCV generally has lower average squared error when disturbances are correlated.

Supplementary materials are available online.     

The Lévy Swap Market Model

Models driven by Lévy processes are attractive since they allow for better statistical fitting than classical diffusion models. The dynamics of the forward swap rate process is derived in a semimartingale setting and a Lévy swap market model is introduced. In order to guarantee positive rates, the swap rates are modelled as ordinary exponentials. The model starts with the most distant rate, which is driven by a non‐homogeneous Lévy process. Via backward induction the remaining swap rates are constructed such that they become martingales under the corresponding forward swap measures. Finally it is shown how swaptions can be priced using bilateral Laplace transforms.     

Bonds and Options in Exponentially Affine Bond Models

Abstract

In this article we apply the Flesaker–Hughston approach to invert the yield curve and to price various options by letting the randomness in the economy be driven by a process closely related to the short rate, called the abstract short rate. This process is a pure deterministic translation of the short rate itself, and we use the deterministic shift to calibrate the models to the initial yield curve. We show that we can solve for the shift needed in closed form by transforming the problem to a new probability measure. Furthermore, when the abstract short rate follows a Cox–Ingersoll–Ross (CIR) process we compute bond option and swaption prices in closed form. We also propose a short-rate specification under the risk-neutral measure that allows the yield curve to be inverted and is consistent with the CIR dynamics for the abstract short rate, thus giving rise to closed form bond option and swaption prices.     

Local Volatility Pricing Models for Long-Dated FX Derivatives

Abstract

We study the local volatility function in the foreign exchange (FX) market, where both domestic and foreign interest rates are stochastic. This model is suitable to price long-dated FX derivatives. We derive the local volatility function and obtain several results that can be used for the calibration of this local volatility on the FX option's market. Then, we study an extension to obtain a more general volatility model and propose a calibration method for the local volatility associated with this model.