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Journal ArticleDOI

New frontiers for arch models

01 Sep 2002-Journal of Applied Econometrics (John Wiley & Sons, Ltd)-Vol. 17, Iss: 5, pp 425-446
TL;DR: In the 20 years following the publication of the ARCH model, there has been a vast quantity of research uncovering the properties of competing volatility models as mentioned in this paper, including high-frequency volatility models, large-scale multivariate ARCH models, and derivatives pricing models.
Abstract: In the 20 years following the publication of the ARCH model, there has been a vast quantity of research uncovering the properties of competing volatility models. Wide-ranging applications to financial data have discovered important stylized facts and illustrated both the strengths and weaknesses of the models. There are now many surveys of this literature. This paper looks forward to identify promising areas of new research. The paper lists five new frontiers. It briefly discusses three—high-frequency volatility models, large-scale multivariate ARCH models, and derivatives pricing models. Two further frontiers are examined in more detail—application of ARCH models to the broad class of non-negative processes, and use of Least Squares Monte Carlo to examine non-linear properties of any model that can be simulated. Using this methodology, the paper analyses more general types of ARCH models, stochastic volatility models, long-memory models and breaking volatility models. The volatility of volatility is defined, estimated and compared with option-implied volatilities. Copyright © 2002 John Wiley & Sons, Ltd.

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Citations
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Journal ArticleDOI
TL;DR: In this article, the authors propose a new approach to quantile estimation which does not require any of the extreme assumptions invoked by existing methodologies (such as normality or i.i.d. returns).
Abstract: Value at Risk (VaR) has become the standard measure of market risk employed by financial institutions for both internal and regulatory purposes. VaR is defined as the value that a portfolio will lose with a given probability, over a certain time horizon (usually one or ten days). Despite its conceptual simplicity, its measurement is a very challenging statistical problem and none of the methodologies developed so far give satisfactory solutions. Interpreting the VaR as the quantile of future portfolio values conditional on current information, we propose a new approach to quantile estimation which does not require any of the extreme assumptions invoked by existing methodologies (such as normality or i.i.d. returns). The Conditional Autoregressive Value-at-Risk or CAViaR model moves the focus of attention from the distribution of returns directly to the behavior of the quantile. We specify the evolution of the quantile over time using a special type of autoregressive process and use the regression quantile framework introduced by Koenker and Bassett to determine the unknown parameters. Since the objective function is not differentiable, we use a differential evolutionary genetic algorithm for the numerical optimization. Utilizing the criterion that each period the probability of exceeding the VaR must be independent of all the past information, we introduce a new test of model adequacy, the Dynamic Quantile test. Applications to simulated and real data provide empirical support to this methodology and illustrate the ability of these algorithms to adapt to new risk environments.

1,834 citations

Journal ArticleDOI
TL;DR: A review of the past 25 years of research into time series forecasting can be found in this paper, where the authors highlight results published in journals managed by the International Institute of Forecasters.

1,383 citations


Cites background from "New frontiers for arch models"

  • ...It would also be useful to examine the volatility-forecasting performance of multivariate GARCH-type models and multivariate nonlinear models, incorporating both temporal and contemporaneous dependencies; see also Engle (2002) for some further possible areas of new research....

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Journal ArticleDOI
TL;DR: In this article, the authors provide a framework for non-parametric measurement of the jump component in asset return volatility and find that jumps are both highly prevalent and distinctly less persistent than the continuous sample path variation process.
Abstract: A rapidly growing literature has documented important improvements in financial return volatility measurement and forecasting via use of realized variation measures constructed from high-frequency returns coupled with simple modeling procedures. Building on recent theoretical results in Barndorff-Nielsen and Shephard (2004a, 2005) for related bi-power variation measures, the present paper provides a practical and robust framework for non-parametrically measuring the jump component in asset return volatility. In an application to the DM/$ exchange rate, the S&P500 market index, and the 30-year U.S. Treasury bond yield, we find that jumps are both highly prevalent and distinctly less persistent than the continuous sample path variation process. Moreover, many jumps appear directly associated with specific macroeconomic news announcements. Separating jump from non-jump movements in a simple but sophisticated volatility forecasting model, we find that almost all of the predictability in daily, weekly, and monthly return volatilities comes from the non-jump component. Our results thus set the stage for a number of interesting future econometric developments and important financial applications by separately modeling, forecasting, and pricing the continuous and jump components of the total return variation process.

1,167 citations

Journal ArticleDOI
TL;DR: In this article, a computer program for modelling financial time series is presented, based on the Random Walk Hypothesis, which is used to forecast trends in prices in futures markets.
Abstract: Features of Financial Returns Modelling Price Volatility Forecasting Standard Deviations The Accuracy of Autocorrelation Estimates Testing the Random Walk Hypothesis Forecasting Trends in Prices Evidence Against the Efficiency of Futures Markets Valuing Options Appendix: A Computer Program for Modelling Financial Time Series.

1,115 citations

Journal ArticleDOI
TL;DR: A unified and consistent framework for introducing time-varying parameters in a wide class of non-linear models, referred to as Generalized Autoregressive Score (GAS) models, which encompasses other well-known models such as the generalized autoregressive conditional heteroskedasticity.
Abstract: We propose a class of observation driven time series models referred to as Generalized Autoregressive Score (GAS) models. The mechanism to update the parameters over time is the scaled score of the likelihood function. This new approach provides a unified and consistent framework for introducing time-varying parameters in a wide class of non-linear models. The GAS model encompasses other well-known models such as the generalized autoregressive conditional heteroskedasticity, the autoregressive conditional duration, the autoregressive conditional intensity, and Poisson count models with time-varying mean. In addition, our approach can lead to new formulations of observation driven models. We illustrate our framework by introducing new model specifications for time-varying copula functions and for multivariate point processes with time-varying parameters. We study the models in detail and provide simulation and empirical evidence.

758 citations


Cites background or methods from "New frontiers for arch models"

  • ...…and intensity (ACD and ACI, respectively) models of Engle and Russell (1998) and Russell (2001), the dynamic conditional correlation (DCC) model of Engle (2002a), the Poisson count models discussed by Davis, Dunsmuir, and Streett (2003), the dynamic copula models of Patton (2006), and the…...

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  • ...(12) This specification is equivalent to the multiplicative error model (MEM) proposed by Engle (2002b) and extended in Engle and Gallo (2006)....

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References
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Journal ArticleDOI
TL;DR: In this article, a parameter covariance matrix estimator which is consistent even when the disturbances of a linear regression model are heteroskedastic is presented, which does not depend on a formal model of the structure of the heteroSkewedness.
Abstract: This paper presents a parameter covariance matrix estimator which is consistent even when the disturbances of a linear regression model are heteroskedastic. This estimator does not depend on a formal model of the structure of the heteroskedasticity. By comparing the elements of the new estimator to those of the usual covariance estimator, one obtains a direct test for heteroskedasticity, since in the absence of heteroskedasticity, the two estimators will be approximately equal, but will generally diverge otherwise. The test has an appealing least squares interpretation.

25,689 citations

Journal ArticleDOI
TL;DR: In this article, a new class of stochastic processes called autoregressive conditional heteroscedastic (ARCH) processes are introduced, which are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances.
Abstract: Traditional econometric models assume a constant one-period forecast variance. To generalize this implausible assumption, a new class of stochastic processes called autoregressive conditional heteroscedastic (ARCH) processes are introduced in this paper. These are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances. For such processes, the recent past gives information about the one-period forecast variance. A regression model is then introduced with disturbances following an ARCH process. Maximum likelihood estimators are described and a simple scoring iteration formulated. Ordinary least squares maintains its optimality properties in this set-up, but maximum likelihood is more efficient. The relative efficiency is calculated and can be infinite. To test whether the disturbances follow an ARCH process, the Lagrange multiplier procedure is employed. The test is based simply on the autocorrelation of the squared OLS residuals. This model is used to estimate the means and variances of inflation in the U.K. The ARCH effect is found to be significant and the estimated variances increase substantially during the chaotic seventies.

20,728 citations

Journal ArticleDOI
TL;DR: In this paper, a natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in 1982 to allow for past conditional variances in the current conditional variance equation is proposed.

17,555 citations

Journal ArticleDOI
TL;DR: In this article, an exponential ARCH model is proposed to study volatility changes and the risk premium on the CRSP Value-Weighted Market Index from 1962 to 1987, which is an improvement over the widely-used GARCH model.
Abstract: This paper introduces an ARCH model (exponential ARCH) that (1) allows correlation between returns and volatility innovations (an important feature of stock market volatility changes), (2) eliminates the need for inequality constraints on parameters, and (3) allows for a straightforward interpretation of the "persistence" of shocks to volatility. In the above respects, it is an improvement over the widely-used GARCH model. The model is applied to study volatility changes and the risk premium on the CRSP Value-Weighted Market Index from 1962 to 1987. Copyright 1991 by The Econometric Society.

10,019 citations


"New frontiers for arch models" refers methods in this paper

  • ...The most influential models were the first: the GARCH model of Bollerslev(1986), and the EGARCH of Nelson(1991)....

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Journal ArticleDOI
Steven L. Heston1
TL;DR: In this paper, a closed-form solution for the price of a European call option on an asset with stochastic volatility is derived based on characteristi c functions and can be applied to other problems.
Abstract: I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset’s price is important for explaining return skewness and strike-price biases in the BlackScholes (1973) model. The solution technique is based on characteristi c functions and can be applied to other problems.

7,867 citations


"New frontiers for arch models" refers methods in this paper

  • ...It is a discrete time analogue of square root diffusion models used by Cox Ingersoll and Ross(1085) , Heston(1993) and many others....

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