Using The Nelson and Siegel Model of The term Structure in Value at Risk Estimation

Over the past decade, no other tool in financial risk management has been used as much as Value at Risk (VaR). VaR is an estimate to determine how much a specific portfolio can lose within a given time period at a given confidence level. Nowadays, in order to improve the performance of VaR methodologies, researchers have suggested numerous modifications of traditional techniques. Following this tendency, this paper explores the use of the model proposed by Nelson and Siegel (with the aim to estimate the term structure of interest rate, TSIR) to implement a simulation to calculate the VaR of a fixed income portfolio. In this approach the dimension of the problem is reduced as the price of the portfolio depends on a vector of four parameters. Subsequently, we can use Monte Carlo simulation techniques to generate future scenarios in these parameters and use them to reevaluate the portfolio. The resulting changes in portfolio value are arranged and the appropriate percentile is determined to provide the VaR estimate. Despite the fact that this approach theoretically facilitates the calculation of VaR on fixed income portfolios, we show that the PROBLEM in practise ignores price sensitivities. So this method cannot therefore be used to calculate VaR on fixed income portfolios.Value at Risk, Financial risk.

Irreducible Lie-Yamaguti algebras

Lie-Yamaguti algebras (or generalized Lie triple systems) are binary-ternary algebras intimately related to reductive homogeneous spaces. The Lie-Yamaguti algebras which are irreducible as modules over their Lie inner derivation algebra are the algebraic counterpart of the isotropy irreducible homogeneous spaces. These systems will be shown to split into three disjoint types: adjoint type, non-simple type and generic type. The systems of the first two types will be classified and most of them will be shown to be related to a Generalized Tits Construction of Lie algebras.Comment: 25 page

Spinozian Intellectual Joy

Este artículo se centra en el gozo intelectual spinoziano. Después de un breve repaso de un libro de Jorge Wagensberg sobre la experiencia del gozo intelectual, aludo al fenómeno contrario: el pensamiento sombrío y el pesimismo. Después, remarco la defensa de Spinoza del gozo del conocimiento y su poder contra la tristeza y el pesimismo. Finalmente, analizo el peculiar gozo intelectual en Spinoza (el tercer género de conocimiento) y conecto este gozo con la experiencia de eternidad y su expresión a través de categorías espaciales.This article is focussed on the intellectual joy in Spinoza. After a brief review of Jorge Wagensberg’s book about the experience of the intellectual joy, I allude to the opposite phenomenon: the dismal thought and pessimism. Then, I remark the Spinoza´s defence of the knowledge´s joy and his power against the sadness and the pessimism. Finally, I analyse the peculiar intellectual joy in Spinoza (the third kind of knowledge) and I connect this joy with the experience of eternity and his expression through spatial categories

Examples and patterns on quadratic Lie algebras

A Lie algebra is said to be quadratic if it admits a symmetric invariant and non-degenerated bilinear form. Semisimple algebras with the Killing form are examples of these algebras, while orthogonal subspaces provide abelian quadatric algebras. The class of quadratic algebras is outsize, but at first sight it is not clear weather an algebra is quadratic. Some necessary structural conditions appear due to the existence of an invariant form forces elemental patterns. Along the paper we overview classical features and constructions on this topic and focus on the existence and constructions of local quadratic

Valor en Riesgo en carteras de renta fija: una comparación entre modelos empíricos de la estructura temporal

En este trabajo se compara la precisión de diferentes medidas de Valor en Riesgo (VaR) en carteras de renta fija calculadas a partir de diferentes modelos empíricos multifactoriales de la estructura temporal de los tipos de interés (ETTI). Los modelos incluidos en la comparativa son tres: (1) modelos de regresión, (2) componentes principales y (3) paramétricos. Adicionalmente, se incluye el sistema de cartografía que utiliza Riskmetrics. Dado que el cálculo de las medidas VaR con dichos modelos requiere el uso de una medida de volatilidad, en este trabajo se utilizan tres medidas distintas: medias móviles exponenciales, medias móviles equiponderadas y modelos GARCH. Por consiguiente, la comparación de la precisión de las medidas VaR tiene dos dimensiones: el modelo multifactorial y la medida de volatilidad. Respecto a los modelos multifactoriales, la evidencia presentada indica que el sistema de mapping o cartografía es el modelo más preciso cuando se calculan medidas VaR (5%). Por el contrario, a un nivel de confianza del 1% el modelo paramétrico (modelo de Nelson y Siegel) es el que genera medidas VaR más precisas. Respecto a las medidas de volatilidad los resultados indican que en general no hay una medida que funcione sistemáticamente mejor que el resto en todos los modelos. Salvo alguna excepción, los resultados obtenidos son independientes del horizonte para el cual se calcula el VaR, ya sea uno o diez días.Value at Risk (VaR), Modelos factoriales, Gestión de riesgo.