1,721,006 research outputs found
A simple approach to the estimation of Tukey's gh distribution
No full textThe Tukey's gh distribution is widely used in situations where skewness and elongation are important features of the data. As the distribution is defined through a quantile transformation of the normal, the likelihood function cannot be written in closed form and exact maximum likelihood estimation is unfeasible. In this paper we exploit a novel approach based on a frequentist reinterpretation of Approximate Bayesian Computation for approximating the maximum likelihood estimates of the gh distribution. This method is appealing because it only requires the ability to sample the distribution. We discuss the choice of the input parameters by means of simulation experiments and provide evidence of superior performance in terms of Root-Mean-Square-Error with respect to the standard quantile estimator. Finally, we give an application to operational risk measurement
Estimating and Forecasting Conditional Risk Measures with Extreme Value Theory: A Review
No full textOne of the key components of financial risk management is risk measurement. This typically requires modeling, estimating and forecasting tail-related quantities of the asset returns’ conditional distribution. Recent advances in the financial econometrics literature have developed several models based on Extreme Value Theory (EVT) to carry out these tasks. The purpose of this paper is to review these methods
Realizing the extremes: Estimation of tail-risk measures from a high-frequency perspective
Full text linkThis article applies realized volatility forecasting to Extreme Value Theory (EVT). We propose a two-step approach where returns are first pre-whitened with a high-frequency based volatility model, and then an EVT based model is fitted to the tails of the standardized residuals. This realized EVT approach is compared to the conditional EVT of McNeil & Frey (2000). We assess both approaches' ability to filter the dependence in the extremes and to produce stable out-of-sample VaR and ES estimates for one-day and ten-day time horizons. The main finding is that GARCH-type models perform well in filtering the dependence, while the realized EVT approach seems preferable in forecasting, especially at longer time horizons
US stock returns: are there seasons of excesses?
No full textThis article explores the existence of seasonality in the tails of stock returns. We use a parametric model to describe the returns, and obtain a proxy of the innovation distribution via a pre-processing model. Then, we develop a change-point algorithm capturing changes in the tails of the innovations. We confirm the good performance of the procedure through extensive Monte Carlo experiments. An empirical investigation using US stocks data shows that while the lower tail of the innovations is approximately constant over the year, the upper tail is larger in Winter than in Summer, in 9 out of 12 industries
Finanza quantitativa con R
No full textIl libro tratta i principali temi della finanza quantitativa partendo dai concetti elementari, fino a toccare argomenti relativamente avanzati nell'ambito del pricing di strumenti finanziari e della misurazione del rischio. Lo scopo del testo è quello di presentare i risultati fondamentali della finanza quantitativa ed illustrarne l'applicazione a dati reali mediante il software statistico R. Il testo bilancia la trattazione teorica degli argomenti, con la presenza di esempi ampiamente ed approfonditamente discussi. Il livello del testo corrisponde a quello di un laboratorio di finanza quantitativa di un corso di laurea magistrale in finanza.The book deals with the main issues of quantitative finance, from the basis to more advanced topics on asset pricing and financial risk measurement. Illustrating the main theoretical results of quantitative finance and providing a method to apply them to real data are the goals of this book. The use of statistical software R is illustrated both from a general perspective, and through many detailed examples based on real data. The level of the treatment is suited for students of master’s degrees in finance
A characteristic function-based approach to approximate maximum likelihood estimation
No full textThe choice of the summary statistics in approximate maximum likelihood is often a crucial issue. We develop a criterion for choosing the most effective summary statistic and then focus on the empirical characteristic function. In the iid setting, the approximating posterior distribution converges to the approximate distribution of the parameters conditional upon the empirical characteristic function. Simulation experiments suggest that the method is often preferable to numerical maximum likelihood. In a time-series framework, no optimality result can be proved, but the simulations indicate that the method is effective in small samples
A Cross-Entropy Approach to the Estimation of Generalised Linear Multilevel Models
Full text linkIn this paper we use the cross-entropy method for noisy optimisation for fitting generalised linear multilevel models through maximum likelihood. We propose specifications of the instrumental distributions for positive and bounded parameters that improve the computational performance. We also introduce a new stopping criterion, which has the advantage of being problem-independent. In a second step we find, by means of extensive Monte Carlo experiments, the most suitable values of the input parameters of the algorithm. Finally, we compare the method to benchmark estimation technique based on numerical integration. The cross-entropy approach turns out to be preferable from both the statistical and the computational point of view. In the last part of the paper, the method is used to model death probability of firms in the healthcare industry in Italy
A Cross-Entropy Approach to the Estimation of Generalized Linear Multilevel Models
No full textIn this article, we use the cross-entropy method for noisy optimization for fitting generalized linear multilevel models through maximum likelihood. We propose specifications of the instrumental distributions for positive and bounded parameters that improve the computational performance. We also introduce a new stopping criterion, which has the advantage of being problem-independent. In a second step we find, by means of extensive Monte Carlo experiments, the most suitable values of the input parameters of the algorithm. Finally, we compare the method to the benchmark estimation technique based on numerical integration. The cross-entropy approach turns out to be preferable from both the statistical and the computational point of view. In the last part of the article, the method is used to model the probability of firm exits in the healthcare industry in Italy. Supplemental materials are available online
Realized peaks over threshold: A time-varying extreme value approach with high-frequency-based measures
No full textRecent contributions to the financial econometrics literature exploit high-frequency (HF) data to improve models for daily asset returns. This paper proposes a new class of dynamic extreme value models that profit from HF data when estimating the tails of daily asset returns. Our realized peaks-over-threshold approach provides estimates for the tails of the time-varying conditional return distribution. An in-sample fit to the S&P 500 index returns suggests that HF data convey information on daily extreme returns beyond that included in low frequency (LF) data. Finally, out-of-sample forecasts of conditional risk measures obtained with HF measures outperform those obtained with LF measures
Testing for Asymmetries and Anisotropies in Regional Economic Models
Full text linkThis paper develops a new methodology for estimating and testing the form of anisotropy of homogeneous spatial processes. We derive a generalised version of the isotropy test proposed by Arbia, Bee and Espa (2013) and analyse its properties in various settings. In light of this, we propose a new approach that allows one to estimate and test under mild conditions any form of anisotropy in homogeneous spatial processes. The power of the test is studied by means of Monte Carlo simulations performed both on regularly and irregularly spaced data. Finally, the method is used to analyse the soybeans yields in the US
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