Credit risk contributions under the Vasicek one-factor model: a fast wavelet expansion approximation

To measure the contribution of individual transactions inside the total risk of a credit portfolio is a major issue in financial institutions. VaR Contributions (VaRC) and Expected Shortfall Contributions (ESC) have become two popular ways of quantifying the risks. However, the usual Monte Carlo (MC) approach is known to be a very time consuming method for computing these risk contributions. In this paper we consider the Wavelet Approximation (WA) method for Value at Risk (VaR) computation presented in [Mas10] in order to calculate the Expected Shortfall (ES) and the risk contributions under the Vasicek one-factor model framework. We decompose the VaR and the ES as a sum of sensitivities representing the marginal impact on the total portfolio risk. Moreover, we present technical improvements in the Wavelet Approximation (WA) that considerably reduce the computational effort in the approximation while, at the same time, the accuracy increases.

Calibration of stochastic volatility models via second order approximation: the Heston model case

Using a suitable Hull and White type formula we develop a methodology to obtain asecond order approximation to the implied volatility for very short maturities. Using thisapproximation we accurately calibrate the full set of parameters of the Heston model. Oneof the reasons that makes our calibration for short maturities so accurate is that we alsotake into account the term-structure for large maturities. We may say that calibration isnot "memoryless", in the sense that the option's behavior far away from maturity doesinfluence calibration when the option gets close to expiration. Our results provide a wayto perform a quick calibration of a closed-form approximation to vanilla options that canthen be used to price exotic derivatives. The methodology is simple, accurate, fast, andit requires a minimal computational cost.

A decomposition formula for option prices in the Heston model and applications to option pricing approximation

By means of classical Itô's calculus we decompose option prices asthe sum of the classical Black-Scholes formula with volatility parameterequal to the root-mean-square future average volatility plus a term dueby correlation and a term due to the volatility of the volatility. Thisdecomposition allows us to develop first and second-order approximationformulas for option prices and implied volatilities in the Heston volatilityframework, as well as to study their accuracy. Numerical examples aregiven.

Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model

Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel equation for the logarithmic interaction kernel in any dimension in the sub-critical case. Moreover, we show how this method performs numerically in one dimension. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudo-inverse of the cumulative distribution function. We demonstrate its capabilities to reproduce easily without the need of mesh-refinement the blow-up of solutions for super-critical masses.

The Total fiscal cost of indirect taxation: an approximation using Catalonia's recent input-output table

In this note we quantify to what extent indirect taxation influences and distorts prices. To do so we use the networked accounting structure of the most recent input-output table of Catalonia, an autonomous region of Spain, to model price formation. The role of indirect taxation is considered both from a classical value perspective and a more neoclassical flavoured one. We show that they would yield equivalent results under some basic premises. The neoclassical perspective, however, offers a bit more flexibility to distinguish among different tax figures and hence provide a clearer disaggregate picture of how an indirect tax ends up affecting, and by how much, the cost structure.

Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the innite d-regular tree. ore recently Sly [8] (see also [1]) showed that this is optimal in the sense that if here is an FPRAS for the hard-core partition function on graphs of maximum egree d for activities larger than the critical activity on the innite d-regular ree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. his in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al [7] to the case of general two-state anti-ferromagnetic spin systems.

L’eficàcia rehabilitadora de la pena de treballs en benefici a la comunitat. Avaluació del model d’execució a la província de Barcelona

El present treball aspira a servir com primera aproximació a una avaluació del model actual d'execució de la pena de Treballs en Benefici de la Comunitat en el nostre actual sistema de penes, a partir de la valoració sobre la presència dels elements que la investigació criminològica ha destacat com a rellevants en matèria de rehabilitació amb penats condemnats a penes de treball comunitari. D’aquesta manera, hem optat per realitzar una investigació qualitativa mitjançant entrevistes a una mostra de penats que van finalitzar el compliment d'una pena de TBC a la província de Barcelona entre el mes d'octubre de 2008 i el de gener de 2009 per tal de conèixer la seva percepció sobre la presència d’aquests elements.

Fronts from two-dimensional dispersal kernels: Beyond the nonoverlapping-generations model

Most integrodifference models of biological invasions are based on the nonoverlapping-generations approximation. However, the effect of multiple reproduction events overlapping generations on the front speed can be very important especially for species with a long life spam . Only in one-dimensional space has this approximation been relaxed previously, although almost all biological invasions take place in two dimensions. Here we present a model that takes into account the overlapping generations effect or, more generally, the stage structure of the population , and we analyze the main differences with the corresponding nonoverlappinggenerations results

Nuclear magnetic resonance chemical shifts with the statistical average of orbital-dependent model potentials in Kohn-Sham density functional theory

The performance of the SAOP potential for the calculation of NMR chemical shifts was evaluated. SAOP results show considerable improvement with respect to previous potentials, like VWN or BP86, at least for the carbon, nitrogen, oxygen, and fluorine chemical shifts. Furthermore, a few NMR calculations carried out on third period atoms (S, P, and Cl) improved when using the SAOP potential

A generalization of Hull and White formula and applications to option pricing approximation

By means of Malliavin Calculus we see that the classical Hull and White formulafor option pricing can be extended to the case where the noise driving thevolatility process is correlated with the noise driving the stock prices. Thisextension will allow us to construct option pricing approximation formulas.Numerical examples are presented.

Adaptive model selection using empirical complexities

Given $n$ independent replicates of a jointly distributed pair $(X,Y)\in {\cal R}^d \times {\cal R}$, we wish to select from a fixed sequence of model classes ${\cal F}_1, {\cal F}_2, \ldots$ a deterministic prediction rule $f: {\cal R}^d \to {\cal R}$ whose risk is small. We investigate the possibility of empirically assessingthe {\em complexity} of each model class, that is, the actual difficulty of the estimation problem within each class. The estimated complexities are in turn used to define an adaptive model selection procedure, which is based on complexity penalized empirical risk.The available data are divided into two parts. The first is used to form an empirical cover of each model class, and the second is used to select a candidate rule from each cover based on empirical risk. The covering radii are determined empirically to optimize a tight upper bound on the estimation error. An estimate is chosen from the list of candidates in order to minimize the sum of class complexity and empirical risk. A distinguishing feature of the approach is that the complexity of each model class is assessed empirically, based on the size of its empirical cover.Finite sample performance bounds are established for the estimates, and these bounds are applied to several non-parametric estimation problems. The estimates are shown to achieve a favorable tradeoff between approximation and estimation error, and to perform as well as if the distribution-dependent complexities of the model classes were known beforehand. In addition, it is shown that the estimate can be consistent,and even possess near optimal rates of convergence, when each model class has an infinite VC or pseudo dimension.For regression estimation with squared loss we modify our estimate to achieve a faster rate of convergence.

A territorial model of commuting in Catalonia, 1986-1996

Commuting consists in the fact that an important fraction of workers in developed countries do not reside close to their workplaces but at long distances from them, so they have to travel to their jobs and then back home daily. Although most workers hold a job in the same municipality where they live or in a neighbouring one, an important fraction of workers face long daily trips to get to their workplace and then back home.Even if we divide Catalonia (Spain) in small aggregations of municipalities, trying to make them as close to local labour markets as possible, we will find out that some of them have a positive commuting balance, attracting many workers from other areas and providing local jobs for almost all their resident workers. On the other side, other zones seem to be mostly residential, so an important fraction of their resident workers hold jobs in different local labour markets. Which variables influence an area¿s role as an attraction pole or a residential zone? In previous papers (Artís et al, 1998a, 2000; Romaní, 1999) we have brought out the main individual variables that influence commuting by analysing a sample of Catalan workers and their commuting decisions. In this paper we perform an analysis of the territorial variables that influence commuting, using data for aggregate commuting flows in Catalonia from the 1991 and 1996 Spanish Population Censuses.These variables influence commuting in two different ways: a zone with a dense, welldeveloped economical structure will have a high density of jobs. Work demand cannot be fulfilled with resident workers, so it spills over local boundaries. On the other side, this economical activity has a series of side-effects like pollution, congestion or high land prices which make these areas less desirable to live in. Workers who can afford it may prefer to live in less populated, less congested zones, where they can find cheaper land, larger homes and a better quality of life. The penalty of this decision is an increased commuting time. Our aim in this paper is to highlight the influence of local economical structure and amenities endowment in the workplace-residence location decision. A place-to-place logit commuting models is estimated for 1991 and 1996 in order to find the economical and amenities variables with higher influence in commuting decisions. From these models, we can outline a first approximation to the evolution of these variables in the 1986-1996 period. Data have been obtained from aggregate flow travel-matrix from the 1986, 1991 and 1996 Spanish Population Censuses

A territorial model of commuting in Catalonia, 1986-1996

Commuting consists in the fact that an important fraction of workers in developed countries do not reside close to their workplaces but at long distances from them, so they have to travel to their jobs and then back home daily. Although most workers hold a job in the same municipality where they live or in a neighbouring one, an important fraction of workers face long daily trips to get to their workplace and then back home.Even if we divide Catalonia (Spain) in small aggregations of municipalities, trying to make them as close to local labour markets as possible, we will find out that some of them have a positive commuting balance, attracting many workers from other areas and providing local jobs for almost all their resident workers. On the other side, other zones seem to be mostly residential, so an important fraction of their resident workers hold jobs in different local labour markets. Which variables influence an area¿s role as an attraction pole or a residential zone? In previous papers (Artís et al, 1998a, 2000; Romaní, 1999) we have brought out the main individual variables that influence commuting by analysing a sample of Catalan workers and their commuting decisions. In this paper we perform an analysis of the territorial variables that influence commuting, using data for aggregate commuting flows in Catalonia from the 1991 and 1996 Spanish Population Censuses.These variables influence commuting in two different ways: a zone with a dense, welldeveloped economical structure will have a high density of jobs. Work demand cannot be fulfilled with resident workers, so it spills over local boundaries. On the other side, this economical activity has a series of side-effects like pollution, congestion or high land prices which make these areas less desirable to live in. Workers who can afford it may prefer to live in less populated, less congested zones, where they can find cheaper land, larger homes and a better quality of life. The penalty of this decision is an increased commuting time. Our aim in this paper is to highlight the influence of local economical structure and amenities endowment in the workplace-residence location decision. A place-to-place logit commuting models is estimated for 1991 and 1996 in order to find the economical and amenities variables with higher influence in commuting decisions. From these models, we can outline a first approximation to the evolution of these variables in the 1986-1996 period. Data have been obtained from aggregate flow travel-matrix from the 1986, 1991 and 1996 Spanish Population Censuses

Deformed-jellium model for the fission of multiply charged metal clusters

A deformed-jellium model is used to calculate the fission barrier height of positive doubly charged sodium clusters within an extended Thomas-Fermi approximation. The fissioning cluster is continuously deformed from the parent configuration until it splits into two fragments. Although the shape of the fission barrier obviously depends on the parametrization of the fission path, we have found that remarkably, the maximum of the barrier corresponds to a configuration in which the emerging fragments are already formed and rather well apart. The implication of this finding in the calculation of critical numbers for fission is illustrated in the case of multiply charged Na clusters.

Dynamically generated open-charm baryons beyond the zero-range approximation

The interaction of the low-lying pseudoscalar mesons with the ground-state baryons in the charm sector is studied within a coupled-channel approach using a t-channel vector-exchange driving force. The amplitudes describing the scattering of the pseudoscalar mesons off the ground-state baryons are obtained by solving the Lippmann-Schwinger equation. We analyze in detail the effects of going beyond the t=0 approximation. Our model predicts the dynamical generation of several open-charm baryon resonances in different isospin and strangeness channels, some of which can be clearly identified with recently observed states.