Forecasting S&P 500 Daily Volatility using a Proxy for Downward Price Pressure

This paper decomposes volatility proxies according to upward and downward price movements in high-frequency financial data, and uses this decomposition for forecasting volatility. The paper introduces a simple Garch-type discrete time model that incorporates such high-frequency based statistics into a forecast equation for daily volatility. Analysis of S&P 500 index tick data over the years 1988-2006 shows that taking into account the downward movements improves forecast accuracy significantly. The R2 statistic for evaluating daily volatility forecasts attains a value of 0.80, both for in-sample and out-of-sample prediction.volatility proxy; downward absolute power variation; log-Garch; volatility asymmetry; leverage effect; SP500; volatility forecasting; high-frequency data

Garch Parameter Estimation Using High-Frequency Data

Estimation of the parameters of Garch models for financial data is typically based on daily close-to-close returns. This paper shows that the efficiency of the parameter estimators may be greatly improved by using volatility proxies based on intraday data. The paper develops a Garch quasi maximum likelihood estimator (QMLE) based on these proxies. Examples of such proxies are the realized volatility and the intraday high-low range. Empirical analysis of the S&P 500 index tick data shows that the use of a suitable proxy may reduce the variances of the estimators of the Garch autoregression parameters by a factor 20.volatility estimation; quasi maximum likelihood; volatility proxy; Gaussian QMLE; log-Gaussian QMLE; autoregressive conditional heteroscedasticity

Proxies for daily volatility

High frequency data are often used to construct proxies for the daily volatility in discrete time volatility models. This paper introduces a calculus for such proxies, making it possible to compare and optimize them. The two distinguishing features of the approach are (1) a simple continuous time extension of discrete time volatility models and (2) an abstract definition of volatility proxy. The theory is applied to eighteen years worth of S&P 500 index data. It is used to construct a proxy that outperforms realized volatility.volatility proxy ; realized volatility ; continuous time embedding ; intraday periodicity

Proxies for daily volatility

High frequency data are often used to construct proxies for the daily volatility in discrete time volatility models. This paper introduces a calculus for such proxies, making it possible to compare and optimize them. The two distinguishing features of the approach are (1) a simple continuous time extension of discrete time volatility models and (2) an abstract definition of volatility proxy. The theory is applied to eighteen years worth of S&P 500 index data. It is used to construct a proxy that outperforms realized volatility.Les données de haute fréquence sont souvent employées pour construire des proxies pour la volatilité journalière dans les modèles de volatilité à temps discret. Cet article présente une théorie mathématique pour de telles proxies, rendant possible leur comparaison et leur optimisation. Les particularités de cette approche sont: (1) un prolongement simple au temps continu des modèles de volatilité à temps discret et (2) une définition abstraite de proxy de volatilité. La théorie est appliquée à dix-huit ans de valeurs de l'indice S&P 500. Elle est employée pour construire une proxy qui surpasse la volatilité réalisée

Ranking and Combining Volatility Proxies for Garch and Stochastic Volatility Models

Daily volatility proxies based on intraday data, such as the high-low range and the realized volatility, are important to the specification of discrete time volatility models, and to the quality of their parameter estimation. The main result of this paper is a simple procedure for combining such proxies into a single, highly efficient volatility proxy. The approach is novel in optimizing proxies in relation to the scale factor (the volatility) in discrete time models, rather than optimizing proxies as estimators of the quadratic variation. For the S&P 500 index tick data over the years 1988-2006 the procedure yields a proxy which puts, among other things, more weight on the sum of the highs than on the sum of the lows over ten-minute intervals. The empirical analysis indicates that this finite-grid optimized proxy outperforms the standard five-minute realized volatility by at least 40%, and the limiting case of the square root of the quadratic variation by 25%

Garch Parameter Estimation Using High-Frequency Data

Estimation of the parameters of Garch models for financial data is typically based on daily close-to-close returns. This paper shows that the efficiency of the parameter estimators may be greatly improved by using volatility proxies based on intraday data. The paper develops a Garch quasi maximum likelihood estimator (QMLE) based on these proxies. Examples of such proxies are the realized volatility and the intraday high-low range. Empirical analysis of the S&P 500 index tick data shows that the use of a suitable proxy may reduce the variances of the estimators of the Garch autoregression parameters by a factor 20

Garch Parameter Estimation Using High-Frequency Data

Estimation of the parameters of Garch models for financial data is typically based on daily close-to-close returns. This paper shows that the efficiency of the parameter estimators may be greatly improved by using volatility proxies based on intraday data. The paper develops a Garch quasi maximum likelihood estimator (QMLE) based on these proxies. Examples of such proxies are the realized volatility and the intraday high-low range. Empirical analysis of the S&P 500 index tick data shows that the use of a suitable proxy may reduce the variances of the estimators of the Garch autoregression parameters by a factor 20

Forecasting S&P 500 Daily Volatility using a Proxy for Downward Price Pressure

This paper decomposes volatility proxies according to upward and downward price movements in high-frequency financial data, and uses this decomposition for forecasting volatility. The paper introduces a simple Garch-type discrete time model that incorporates such high-frequency based statistics into a forecast equation for daily volatility. Analysis of S&P 500 index tick data over the years 1988-2006 shows that taking into account the downward movements improves forecast accuracy significantly. The R2 statistic for evaluating daily volatility forecasts attains a value of 0.80, both for in-sample and out-of-sample prediction

Forecasting S&P 500 Daily Volatility using a Proxy for Downward Price Pressure

This paper decomposes volatility proxies according to upward and downward price movements in high-frequency financial data, and uses this decomposition for forecasting volatility. The paper introduces a simple Garch-type discrete time model that incorporates such high-frequency based statistics into a forecast equation for daily volatility. Analysis of S&P 500 index tick data over the years 1988-2006 shows that taking into account the downward movements improves forecast accuracy significantly. The R2 statistic for evaluating daily volatility forecasts attains a value of 0.80, both for in-sample and out-of-sample prediction

Genomic selection on breeding time in a wild bird population

Abstract Artificial selection experiments are a powerful tool in evolutionary biology. Selecting individuals based on multimarker genotypes (genomic selection) has several advantages over phenotype‐based selection but has, so far, seen very limited use outside animal and plant breeding. Genomic selection depends on the markers tagging the causal loci that underlie the selected trait. Because the number of necessary markers depends, among other factors, on effective population size, genomic selection may be in practice not feasible in wild populations as most wild populations have much higher effective population sizes than domesticated populations. However, the current possibilities of cost‐effective high‐throughput genotyping could overcome this limitation and thereby make it possible to apply genomic selection also in wild populations. Using a unique dataset of about 2000 wild great tits (Parus major), a small passerine bird, genotyped on a 650 k SNP chip we calculated genomic breeding values for egg‐laying date using the so‐called GBLUP approach. In this approach, the pedigree‐based relatedness matrix of an “animal model,” a special form of the mixed model, is replaced by a marker‐based relatedness matrix. Using the marker‐based relatedness matrix, the model seemed better able to disentangle genetic and permanent environmental effects. We calculated the accuracy of genomic breeding values by correlating them to the phenotypes of individuals whose phenotypes were excluded from the analysis when estimating the genomic breeding values. The obtained accuracy was about 0.20, with very little effect of the used genomic relatedness estimator but a strong effect of the number of SNPs. The obtained accuracy is lower than typically seen in domesticated species but considerable for a trait with low heritability (∼0.2) as avian breeding time. Our results show that genomic selection is possible also in wild populations with potentially many applications, which we discuss here