The impossibility of strategy-proof clustering

Clustering methods group individuals or objects based on information about their similarity or proximity. When the raw information to generate clusters cannot be easily observed or verified, the cluster designer must rely on information reported by individuals behind the observations. When these individuals receive utility from a public decision taken with aggregated data within each own's cluster and have single-peaked preferences, we prove that there do not exist clustering methods such that truth-revealing behavior is always a dominant strategyclustering methods

Forecasting the density of asset returns

In this paper we introduce a transformation of the Edgeworth-Sargan series expansion of the Gaussian distribution, that we call Positive Edgeworth-Sargan (PES). The main advantage of this new density is that it is well defined for all values in the parameter space, as well as it integrates up to one. We include an illustrative empirical application to compare its performance with other distributions, including the Gaussian and the Student's t, to forecast the full density of daily exchange-rate returns by using graphical procedures. Our results show that the proposed function outperforms the other two models for density forecasting, then providing more reliable value-at-risk forecasts.Density forecasting, Edgeworth-Sargan distribution, probability integral transformations, P-value plots, VaR

Multivariate moments expansion density : application of the dynamic equicorrelation model

En este estudio, proponemos un nuevo tipo de distribución semi-noparamétrica (SNP) para describir la densidad de los rendimientos de las carteras de activos. Esta distribución, denominada «expansión de momentos multivariante» (MME), admite cualquier distribución (multivariante) no-Gausiana como base de la expansión, ya que está directamente especificada en términos de los momentos de dicha distribución. En el caso de la expansión de una distribución normal, la MME es una reformulación de la distribución Gram-Charlier multivariante (MGC), pero, cuando se utilizan transformaciones de positividad para obtener densidades bien definidas, la MME es más sencilla y manejable que la MGC. Como aplicación empírica, extendemos el modelo de equicorrelación dinámica condicional (DECO) a un contexto SNP utilizando la MME. El modelo resultante presenta una formulación sencilla que admite la estimación consistente en dos etapas e incorpora DECO, así como las características no-Gausianas de la distribución de los rendimientos de cartera. La capacidad predictiva del modelo MME-DECO para una cartera de 10 activos demuestra que puede ser una herramienta útil para la gestión y el control del riesgo de carteraIn this study, we propose a new semi-nonparametric (SNP) density model for describing the density of portfolio returns. This distribution, which we refer to as the multivariate moments expansion (MME), admits any non-Gaussian (multivariate) distribution as its basis because it is specified directly in terms of the basis densitys moments. To obtain the expansion of the Gaussian density, the MME is a reformulation of the multivariate Gram-Charlier (MGC), but the MME is much simpler and tractable than the MGC when positive transformations are used to produce well-defined densities. As an empirical application, we extend the dynamic conditional equicorrelation (DECO) model to an SNP framework using the MME. The resulting model is parameterized in a feasible manner to admit two-stage consistent estimation, and it represents the DECO as well as the salient non-Gaussian features of portfolio return distributions. The in- and out-of-sample performance of a MME-DECO model of a portfolio of 10 assets demonstrates that it can be a useful tool for risk management purpose

Multivariate Gram-Charlier Densities

This paper introduces a new family of multivariate distributions based on Gram-Charlier and Edgeworth expansions. This family encompasses many of the univariate seminonparametric densities proposed in the financial econometrics as marginal distributions of the different formulations. Within this family, we focus on the specifications that guarantee positivity so obtaining a well-defined multivariate density. We compare different "positive" multivariate distributions of the family with the multivariate Edgeworth-Sargan, Normal and Student’s t in an in- and out-sample framework for financial returns data. Our results show that the proposed specifications provide a quite reasonably good performance being so of interest for applications involving the modelling and forecasting of heavy-tailed distributions.Multivariate distributions; Gram-Charlier and Edgeworth-Sargan densities; MGARCH models; financial data

Modeling the electricity spot price with switching regime semi-nonparametric distributions

Spot prices of electricity in liberalized markets feature seasonality, mean reversion, random short-term jumps, skewness and highly kurtosis, as a result from the interaction between the supply and demand and the physical restrictions for transportation and storage. To account for such stylized facts, we propose a stochastic process with a component of mean reversion and switching regime to represent the dynamics of the spot price of electricity and its logarithm. The short-term movements are represented by semi-nonparametric (SNP) distributions, in contrast to previous studies that traditionally assume Gaussian processes. The application is done for the Colombian electricity market, where El Niño phenomenon represents an additional source of risk that should be considered to guarantee long-term supply, sustainability of investments and efficiency of prices. We show that the switching regime model with SNP distributions for the random components outperforms traditional models leading to accurate estimates and simulations, and thus being a useful tool for risk management and policy making

Measuring firm size distribution with semi-nonparametric densities

In this article, we propose a new methodology based on a (log) semi-nonparametric (log- SNP) distribution that nests the lognormal and enables better fits in the upper tail of the distribution through the introduction of new parameters. We test the performance of the lognormal and log-SNP distributions capturing firm size, measured through a sample of US firms in 2004-2015. Taking different levels of aggregation by type of economic activity, our study shows that the log-SNP provides a better fit of the firm size distribution. We also formally introduce the multivariate log-SNP distribution, which encompasses the multivariate lognormal, to analyze the estimation of the joint distribution of the value of the firm’s assets and sales. The results suggest that sales are a better firm size measure, as indicated by other studies in the literature

Implicit probability distribution for WTI options: The Black Scholes vs. the semi-nonparametric approach

Este documento contribuye a la literatura sobre la estimación de la función de Densidad de Riesgo Neutral (RND) modelando los precios de las opciones del crudo West Texas Intermediate (WTI) que se comercializaron en el período comprendido entre enero de 2016 y enero de 2017. Para estas series, se extrae la RND implícita en los precios de las opciones aplicando el modelo tradicional Black & Scholes (1973) y el modelo semi-no paramétrico (SNP) propuesto por Backus, Foresi, Li y Wu (1997). Los resultados obtenidos muestran que cuando el precio promedio del mercado se compara con el precio teórico promedio, la especificación lognormal tiende a subestimar sistemáticamente la estimación. Por el contrario, el modelo de fijación de precios SNP, que se ajusta explícitamente a la asimetría negativa y al exceso de curtosis, da como resultado una precisión marcadamente mejorada.This paper contributes to the literature on the estimation of the Risk Neutral Density (RND) function by modeling the prices of options for West Texas Intermediate (WTI) crude oil that were traded in the period between January 2016 and January 2017. For these series we extract the implicit RND in the option prices by applying the traditional Black & Scholes (1973) model and the semi-nonparametric (SNP) model proposed by Backus, Foresi, Li, & Wu (1997). The results obtained show that when the average market price is compared to the average theoretical price, the lognormal specification tends to systematically undervalue the estimation. On the contrary, the SNP option pricing model, which explicitly adjust for negative skewness and excess kurtosis, results in markedly improved accuracy