Models For Financial Returns Research Articles

Gaussian Variational Approximations for High-dimensional State Space Models

We consider a Gaussian variational approximation of the posterior density in high-dimensional state space models. The number of parameters in the covariance matrix of the variational approximation grows as the square of the number of model parameters, so it is necessary to find simple yet effective parametrisations of the covariance structure when the number of model parameters is large. We approximate the joint posterior density of the state vectors by a dynamic factor model, having Markovian time dependence and a factor covariance structure for the states. This gives a reduced description of the dependence structure for the states, as well as a temporal conditional independence structure similar to that in the true posterior. We illustrate the methodology on two examples. The first is a spatio-temporal model for the spread of the Eurasian collared-dove across North America. Our approach compares favorably to a recently proposed ensemble Kalman filter method for approximate inference in high-dimensional hierarchical spatio-temporal models. Our second example is a Wishart-based multivariate stochastic volatility model for financial returns, which is outside the class of models the ensemble Kalman filter method can handle.

History of university radio broadcasting in Turkey and its struggle for legal existence

University radio broadcasting, whose first examples in Turkey date back to the 1940s, made its main leap forward with the emergence of private radio broadcasting in the early 1990s and the increase in the number of communication and broadcasting schools at different levels. Largely unable to exist legally except for a few exceptions, university radio stations have had to deal with many problems from the first examples until today. In this study, we conducted in-depth interviews with the representatives and employees of university radio stations affiliated with 34 universities in Turkey. We found that the lack of a legal basis for university radio stations causes various problems in practice. The most important of these problems include the following: first, the practices of frequency allocation and usage fees by relevant authorities are not conducted in compliance with certain standards. Financial return models are rigid and limited; the production efficiency of a radio station is interrupted when university financial support or station management is irregular or insufficient, as well. As a result, employees experience a loss of motivation in the management and content production stages.

Measurement of common risks in tails: A panel quantile regression model for financial returns

We investigate how to measure common risks in the tails of return distributions using the recently proposed panel quantile regression model for financial returns. By exploring how volatility crosses all quantiles of the return distribution and using a fixed effects estimator, we can control for otherwise unobserved heterogeneity among financial assets. Direct benefits are revealed in a portfolio value-at-risk application, where our modeling strategy performs significantly better than several benchmark models. In particular, our results show that the panel quantile regression model for returns consistently outperforms all competitors in the left tail. Sound statistical performance translates directly into economic gains.

Semiparametric Conditional Quantile Models for Financial Returns and Realized Volatility

This paper investigates how the conditional quantiles of future returns and volatility of financial assets vary with various measures of ex-post variation in asset prices as well as option-implied volatility. We work in the flexible quantile regression framework and rely on recently developed model-free measures of integrated variance, upside and downside semivariance, and jump variation. Our results for the S&P 500 and WTI Crude Oil futures contracts show that simple linear quantile regressions for returns and heterogenous quantile autoregressions for realized volatility perform very well in capturing the dynamics of the respective conditional distributions, both in absolute terms as well as relative to a couple of well-established benchmark models. The models can therefore serve as useful risk management tools for investors trading the futures contracts themselves or various derivative contracts written on realized volatility.

Financial modeling with heavy‐tailed stable distributions

The aim of this article was to give an accessible introduction to stable distributions for financial modeling. There is a real need to use better models for financial returns because the normal (or bell curve/Gaussian) model does not capture the large fluctuations seen in real assets. Stable laws are a class of heavy‐tailed probability distributions that can model large fluctuations and allow more general dependence structures. WIREs Comput Stat 2014, 6:45–55. doi: 10.1002/wics.1286This article is categorized under: Applications of Computational Statistics > Computational Finance Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Robust Methods

Multiple-Change-Point Detection for Auto-Regressive Conditional Heteroscedastic Processes

SummaryThe emergence of the recent financial crisis, during which markets frequently underwent changes in their statistical structure over a short period of time, illustrates the importance of non-stationary modelling in financial time series. Motivated by this observation, we propose a fast, well performing and theoretically tractable method for detecting multiple change points in the structure of an auto-regressive conditional heteroscedastic model for financial returns with piecewise constant parameter values. Our method, termed BASTA (binary segmentation for transformed auto-regressive conditional heteroscedasticity), proceeds in two stages: process transformation and binary segmentation. The process transformation decorrelates the original process and lightens its tails; the binary segmentation consistently estimates the change points. We propose and justify two particular transformations and use simulation to fine-tune their parameters as well as the threshold parameter for the binary segmentation stage. A comparative simulation study illustrates good performance in comparison with the state of the art, and the analysis of the Financial Times Stock Exchange FTSE 100 index reveals an interesting correspondence between the estimated change points and major events of the recent financial crisis. Although the method is easy to implement, ready-made R software is provided.

Empirical Studies in a Multivariate Non-Stationary, Nonparametric Regression Model for Financial Returns

In this paper we analyze a multivariate non-stationary regression model empirically. With the knowledge about unconditional heteroscedasticty of financial returns, based on univariate studies and a congruent paradigm in Gurtler and Rauh (2009), we test for a time-varying covariance structure firstly. Based on these results, a central component of our non-stationary model is a kernel regression for pairwise covariances and the covariance matrix. Residual terms are fitted with an asymmetric Pearson type VII distribution. In an extensive study we estimate the linear dependence of a broad portfolio of equities and fixed income securities (including credit and currency risks) and fit the whole approach to provide distributional forecasts. Our evaluations verify a reasonable approximation and a satisfactory forecasting quality with an out performance against a traditional risk model.

Continuous-Time Skewed Multifractal Processes as a Model for Financial Returns

We present the construction of a continuous-time stochastic process which has moments that satisfy an exact scaling relation, including odd-order moments. It is based on a natural extension of the multifractal random walk construction described in Bacry and Muzy (2003). This allows us to propose a continuous-time model for the price of a financial asset that reflects most major stylized facts observed on real data, including asymmetry and multifractal scaling.

Continuous-Time Skewed Multifractal Processes as a Model for Financial Returns

We present the construction of a continuous-time stochastic process which has moments that satisfy an exact scaling relation, including odd-order moments. It is based on a natural extension of the multifractal random walk construction described in Bacry and Muzy (2003). This allows us to propose a continuous-time model for the price of a financial asset that reflects most major stylized facts observed on real data, including asymmetry and multifractal scaling.

Optimally weighting higher-moment instruments to deal with measurement errors in financial return models

Factor loadings are often measured with errors in financial return models. However, these models find applications in many fields of economics and finance. We present a new procedure to optimally weight two well-known cumulant (higher moments) estimators originally designed to deal with errors-in-variables. We develop a new version of the Hausman test which relies on these new instruments in order to build an indicator of measurement errors providing information about the extent of the bias for an estimated coefficient. We apply our new methodology to a well-known financial return model, i.e. the Fama and French (1997) model, over a sample of Hedge Fund Research (HFR) returns, whose distribution is strongly asymmetric and leptokurtic. Our experiments suggest that the market beta is biased by measurement errors, especially at the level of hedge fund strategies. Nevertheless, the alpha puzzle remains robust to our cumulant instruments.

Optimally weighting higher-moment instruments to deal with measurement errors in financial return models

Optimally weighting higher-moment instruments to deal with measurement errors in financial return models

Density Forecasting with Time‐Varying Higher Moments: A Model Confidence Set Approach

ABSTRACTDensity forecasts contain a complete description of the uncertainty associated with a point forecast and are therefore important measures of financial risk. This paper aims to examine whether the new more complicated models for financial returns that allow for time variation in higher moments lead to better out‐of‐sample density forecasts. Using two decades of daily Standard & Poor's 500 index returns I find that a model with time‐varying conditional variance, skewness and kurtosis produces significantly better density forecasts than the competing models. Copyright © 2011 John Wiley & Sons, Ltd.

Density Forecasting with Time Varying Higher Moments - A Model Confidence Set Approach

Density forecasts contain a complete description of the uncertainty associated with a point forecast and are therefore important measures of financial risk. This paper aims to examine if the new more complicated models for financial returns that allow for time variation in higher moments lead to better out-of-sample density forecasts. Using two decades of daily Standard and Poor's 500 index returns I find that a model with time varying conditional variance, skewness and kurtosis produces significantly better density forecasts than the competing models.

A Non-Stationary Approach for Financial Returns with Nonparametric Heteroscedasticity

A non-stationary regression model for financial returns is examined theoretically. Volatility dynamics are modeled by nonparametric curve estimation on equidistant return vectors. We prove consistency and asymptotic normality of symmetric estimators and of one-sided estimators for variances and covariance matrices analytically, and derive remarks on kernels and bandwidths. Further attention is paid to asymmetry and heavy tails of returns, captured by an asymmetric Pearson type VII distribution for random residuals. Using a method of moments for its parameter estimation and a Student-t connection, a factor-based VaR implementation is derived. The approximation quality of the non-stationary approach is supported by simulation studies.

Value at Risk with time varying variance, skewness and kurtosis-the NIG-ACD model

A new model for financial returns with time varying variance, skewness and kurtosis based on the Normal Inverse Gaussian (NIG) distribution is proposed. The new model and two previously suggested NIG models are evaluated by their Value at Risk (VaR) forecasts on a long series of daily Standard and Poor's 500 returns. All three models perform very well compared with extant models and clearly outperform a Gaussian GARCH model. Moreover, the results show that only the new model cannot be rejected as providing correct conditional VaR forecasts.

Temporal aggregation of Markov‐switching financial return models

AbstractIn this paper we investigate the effects of temporal aggregation of a class of Markov‐switching models known as Markov‐switching normal (MSN) models. The growing popularity of the MSN processes in modelling financial returns can be attributed to their inherited flexibility characteristics, allowing for heteroscedasticity, asymmetry and excess kurtosis. The distributions of the process described by the basic MSN model and the model of the corresponding temporal aggregate data are derived. They belong to a general class of mixture normal distributions. The limiting behaviour of the aggregated MSN model, as the order of aggregation tends to infinity, is studied. We provide explicit formulae for the volatility, autocovariance, skewness and kurtosis of the aggregated processes. An application of measuring solvency risk with MSN models for horizons larger than 1 year and up to 10 years from the baseline U.S. S&P 500 stock market total return time series spanning about 50 years is given. Copyright © 2008 John Wiley & Sons, Ltd.

Stochastic models for risk estimation in volatile markets: a survey

Portfolio risk estimation in volatile markets requires employing fat-tailed models for financial returns combined with copula functions to capture asymmetries in dependence and an appropriate downside risk measure. In this survey, we discuss how these three essential components can be combined together in a Monte Carlo based framework for risk estimation and risk capital allocation with the average value-at-risk measure (AVaR). AVaR is the average loss provided that the loss is larger than a predefined value-at-risk level. We consider in some detail the AVaR calculation and estimation and investigate the stochastic stability.

A Non-Stationary Paradigm for the Dynamics of Multivariate Financial Returns

A simple non-stationary paradigm for the dynamics of multivariate returns is discussed. Unlike most of the multivariate econometric models for financial returns, our approach supposes the volatility to be exogenous and non-stationary. The vectors of returns are assumed to be animated by a slowly changing {making it unconditional} covariance structure. The methodological frame is that of non-parametric regression with fixed, equidistant design points. The regression function is the time evolving unconditional covariance. Special attention is payed to the accurate description of the extremal dependence of the vector of returns. The non-stationary paradigm is first applied to describe the changing dynamics of a multivariate data set of returns on three financial risk factors: a foreign exchange rate, an index and an interest rate. Then, its one-day-ahead multivariate distributional forecast performance is evaluated. We show through an out-of sample simulation experiment that our methodology is superior to the plain-vanilla specification of the industry standard RiskMetrics in forecasting the distribution of returns on portfolios of the three risk factors over horizons of one day, ten days and twenty days.

Nonparametric Inference of Value-at-Risk for Dependent Financial Returns

The article considers nonparametric estimation of value-at-risk (VaR) and associated standard error estimation for dependent financial returns. Theoretical properties of the kernel VaR estimator are investigated in the context of dependence. The presence of dependence affects the variance of the VaR estimates and has to be taken into consideration in order to obtain adequate assessment of their variation. An estimation procedure of the standard errors is proposed based on kernel estimation of the spectral density of a derived series. The performance of the VaR estimators and the proposed standard error estimation procedure are evaluated by theoretical investigation, simulation of commonly used models for financial returns, and empirical studies on real financial return series.

Tail index estimation in small smaples Simulation results for independent and ARCH-type financial return models

Estimation of the tail index of stationary, fat-tailed return distributions is non-trivial since the well-known Hill estimator is optimal only under iid draws from an exact Pareto model. We provide a small sample simulation study of recently suggested adaptive estimators under ARCH-type dependence. The Hill estimator’s performance is found to be dominated by a ratio estimator. Dependence increases estimation error which can remain substantial even in larger data sets. As small sample bias is related to the magnitude of the tail index, recent standard applications may have overestimated (underestimated) the risk of assets with low (high) degrees of fat-tailedness.