Measuring financial risk : comparison of alternative procedures to estimate VaR and ES

We review several procedures for estimating and backtesting two of the most important measures of risk, the Value at Risk (VaR) and the Expected Shortfall (ES). The alternative estimators differ in the way the specify and estimate the conditional mean and variance and the conditional distribution of returns. The results are illustrated by estimating the VaR and ES of daily S&P500 returns

One-loop quantization of rigid spinning strings in AdS3×S3×T4AdS_3 \times S^3 \times T^4 with mixed flux

We compute the one-loop correction to the classical dispersion relation of rigid closed spinning strings with two equal angular momenta in the $AdS_3 \times S^3 \times T^4$ background supported with a mixture of R-R and NS-NS three-form fluxes. This analysis is extended to the case of two arbitrary angular momenta in the pure NS-NS limit. We perform this computation by means of two different methods. The first method relies on the Euler-Lagrange equations for the quadratic fluctuations around the classical solution, while the second one exploits the underlying integrability of the problem through the finite-gap equations. We find that the one-loop correction vanishes in the pure NS-NS limit.Comment: 35 pages. v2: Minor changes and references updated. v3: Published versio

Bootstrap prediction intervals for VaR and ES in the context of GARCH models

In this paper, we propose a new bootstrap procedure to obtain prediction intervals of future Value at Risk (VaR) and Expected Shortfall (ES) in the context of univariate GARCH models. These intervals incorporate the parameter uncertainty associated with the estimation of the conditional variance of returns. Furthermore, they do not depend on any particular assumption on the error distribution. Alternative bootstrap intervals previously proposed in the literature incorporate the first but not the second source of uncertainty when computing the VaR and ES. We also consider an iterated smoothed bootstrap with better properties than traditional ones when computing prediction intervals for quantiles. However, this latter procedure depends on parameters that have to be arbitrarily chosen and is very complicated computationally. We analyze the finite sample performance of the proposed procedure and show that the coverage of our proposed procedure is closer to the nominal than that of the alternatives. All the results are illustrated by obtaining one-step-ahead prediction intervals of the VaR and ES of several real time series of financial returns.Expected Shortfall, Feasible Historical Simulation, Hill estimator, Parameter uncertainty, Quantile intervals, Value at Risk

Measuring financial risk : comparison of alternative procedures to estimate VaR and ES

We review several procedures for estimating and backtesting two of the most important measures of risk, the Value at Risk (VaR) and the Expected Shortfall (ES). The alternative estimators differ in the way the specify and estimate the conditional mean and variance and the conditional distribution of returns. The results are illustrated by estimating the VaR and ES of daily S&P500 returns.Backtesting, Extreme value, GARCH models, Leverage effect

Minimal surfaces with mixed three-form flux

We study minimal area world sheets ending on two concentric circumferences on the boundary of Euclidean $AdS_{3}$ with mixed R-R and NS-NS three-form fluxes. We solve the problem by reducing the system to a one-dimensional integrable model. We find that the NS-NS flux term either brings the surface near to the boundary or separates the circumferences. In the limit of pure NS-NS flux the solution adheres to the boundary in the former case and the outer radius diverges in the latter. We further construct the underlying elliptic spectral curve, which allows us to analyze the deformation of other related minimal surfaces. We show that in the regime of pure NS-NS flux the elliptic curve degenerates.Comment: 15 pages. Latex. v2: Title changed together with minor updates to emphasize that minimal area surfaces in the presence of mixed fluxes are found. v3: Published versio

Pulsating strings with mixed three-form flux

Circular strings pulsating in $AdS_3 \times S^3 \times T^4$ with mixed R-R and NS-NS three-form fluxes can be described by an integrable deformation of the one-dimensional Neumann-Rosochatius mechanical model. In this article we find a general class of pulsating solutions to this integrable system that can be expressed in terms of elliptic functions. In the limit of strings moving in $AdS_{3}$ with pure NS-NS three-form flux, where the action reduces to the $SL(2,\mathbb{R})$ WZW model, we find agreement with the analysis of the classical solutions of the system performed using spectral flow by Maldacena and Ooguri. We use our elliptic solutions in $AdS_{3}$ to extend the dispersion relation beyond the limit of pure NS-NS flux.Comment: 10 pages. Late

The SU(2)SU(2) Wess-Zumino-Witten spin chain sigma model

Classical strings propagating in $AdS_{3}\times S^{3}\times T^{4}$ supported with Neveu-Schwarz-Neveu-Schwarz flux are described by a Wess-Zumino-Witten model. In this note, we study the emergence of their semiclassical $SU(2)$ spectrally flowed sectors as the Landau-Lifshitz limit of the underlying quantum spin chain. We consider the propagator in the coherent state picture, and find that the time interval is discretized proportionally to the lattice spacing. In the Landau-Lifshitz limit, where both time and space become continuous, we derive a path integral representation of the propagator for each spectrally flowed sector. We prove that the arbitrariness of the global phase of coherent states is mapped to the gauge freedom of the $B$-field in the classical action. We show that higher order corrections in the Landau-Lifshitz limit are suppressed by inverse powers of the 't Hooft coupling.Comment: 10 pages, Latex. v2: Published version. v3: Acknowledgement adde

El ensanche occidental de la Córdoba Califal

El presente trabajo recoge de manera generalizada algunas consideraciones en cuanto al urbanismo de los arrabales occidentales de la Qurtuba islámica y la organización interna de la típica vivienda hispanomusulmana, con sus estancias orgnizadas en torno al patio que ejerce de elemento aglutinador, como resultado de las diversas intervenciones arqueológicas desarrolladas a raíz de la expansión urbanística de la Córdoba actual.The present work picks up in a widespread way some considerations as for the urbanism of the western suburbs in the islamis Qurtuba and the internal organization of the typical housing muslim hispanic, with its organized stays around the patio that exercises of agglutinative element, as a result of the diverse archaeological interventions developed soon after the expansion urbanistic of the current Córdoba

Homomástica

En este documento expongo el proceso de trabajo e investigación que he llevado a cabo para realizar el proyecto artístico titulado “Homomástica”. Este término surge de la unión de las palabras “onomástica”1 y “homosexual” y funciona como adelanto del carácter que tiene la obra. Actualmente el colectivo LGBT sigue sin ser aceptado de forma totalmente abierta en todos los ámbitos de nuestra época, especialmente en el entorno religioso. La práctica de la homosexualidad o la transexualidad, por ejemplo, no es aceptada dentro de cualquier ideología anclada en determinadas religiones, llegando incluso a ser objeto de condena y muerte. Mi investigación se centra en concreto en la figura de los homosexuales y el rechazo que sufren por parte de la religión cristiana católica. El principal objetivo del proyecto es señalar esta problemática, hacer consciente al espectador de este hecho a veces normalizado y plantear como respuesta una dignificación de dicha figura (la del homosexual) tan castigada y degradada dentro de esta ideología. Para ello, teniendo como medio plástico la pintura y el uso del collage, creo un universo plástico surrealista, incorporando elementos de la divinidad, en el cual aparecen como personaje principal personas homosexuales reales que han sufrido en su vida algún tipo de rechazo homófobo por parte de miembros de la iglesia católica. Estos personajes aparecen santificados dentro de un ambiente temáticamente invadido por la presencia de distintas ciencias e ingenierías según la obra. Además estas composiciones tienen un trato similar al de la iconografía cristiana e incluyen elementos propios de esta corriente planteándose así el carácter principal de la obra, la ironía. A través del uso del sarcasmo se plantea una visión reflexiva de la obra intentando evitar una actitu