Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model

We propose a dynamic model for the high/low range of asset prices within fixed time intervals: the Conditional Autoregressive Range Model (henceforth CARR). The evolution of the conditional range is specified in a fashion similar to the conditional variance models as in GARCH and is very similar to the Autoregressive Conditional Duration (ACD) model of Engle and Russell (1998). Extreme value theories imply that the range is an efficient estimator of the local volatility, e.g., Parkinson (1980). Hence, CARR can be viewed as a model of volatility. Out-of-sample volatility forecasts using the S&P500 index data show that the CARR model does provide sharper volatility estimates compared with a standard GARCH model.

[1]  Michael W. Brandt,et al.  Volatility Forecasting With Range-Based EGARCH Models , 2006 .

[2]  R. Chou,et al.  Modeling the Asymmetry of Stock Movements Using Price Ranges , 2006 .

[3]  Ruey S. Tsay,et al.  Analysis of Financial Time Series , 2005 .

[4]  R. Engle.  New Frontiers for Arch Models , 2002 .

[5]  Michael W. Brandt,et al.  Range-Based Estimation of Stochastic Volatility Models , 2001 .

[6]  D. Yang,et al.  Drift Independent Volatility Estimation Based on High, Low, Open, and Close Prices , 2000 .

[7]  F. Diebold,et al.  The Distribution of Realized Exchange Rate Volatility , 2000 .

[8]  S. Heston,et al.  A Closed-Form GARCH Option Valuation Model , 2000 .

[9]  Peter E. Rossi,et al.  Modelling stock market volatility : bridging the gap to continuous time , 2000 .

[10]  Alan L. Lewis.  Option Valuation Under Stochastic Volatility: With Mathematica Code , 2000 .

[11]  Francis X. Diebold,et al.  Range-Based Estimation of Stochastic Volatility Models or Exchange Rate Dynamics are More Interesting than You Think , 1999 .

[12]  A. Gallant,et al.  Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance , 1999, Review of Economics and Statistics.

[13]  Peter H. Ritchken,et al.  Pricing Options under Generalized GARCH and Stochastic Volatility Processes , 1999 .

[14]  F. Diebold,et al.  The Distribution of Exchange Rate Volatility , 1999 .

[15]  T. Bollerslev,et al.  ANSWERING THE SKEPTICS: YES, STANDARD VOLATILITY MODELS DO PROVIDE ACCURATE FORECASTS* , 1998 .

[16]  L. Rogers.  Volatility Estimation with Price Quanta , 1998 .

[17]  Jeffrey R. Russell,et al.  Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data , 1998 .

[18]  Jin-Chuan Duan,et al.  Augmented GARCH (p,q) process and its diffusion limit , 1997 .

[19]  David I. Harvey.  The evaluation of economic forecasts , 1997 .

[20]  A. Marathe,et al.  Expected stock returns and volatility in a two-regime market , 1995 .

[21]  J. Duan.  THE GARCH OPTION PRICING MODEL , 1995 .

[22]  Michael S. Rozeff,et al.  Variance, Return, and High-Low Price Spreads , 1994 .

[23]  Tim Bollerslev,et al.  Chapter 49 Arch models , 1994 .

[24]  Daniel B. Nelson,et al.  ARCH MODELS a , 1994 .

[25]  S. Heston.  A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options , 1993 .

[26]  R. Chou,et al.  ARCH modeling in finance: A review of the theory and empirical evidence , 1992 .

[27]  T. Day,et al.  Stock market volatility and the information content of stock index options , 1992 .

[28]  Naoto Kunitomo,et al.  Improving the Parkinson Method of Estimating Security Price Volatilities , 1992 .

[29]  J. Wooldridge,et al.  Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances , 1992 .

[30]  James B. Wiggins.  Empirical tests of the bias and efficiency of the extreme-value variance estimator for common stocks , 1993 .

[31]  L. Rogers,et al.  Estimating Variance From High, Low and Closing Prices , 1991 .

[32]  Daniel B. Nelson.  CONDITIONAL HETEROSKEDASTICITY IN ASSET RETURNS: A NEW APPROACH , 1991 .

[33]  W. Andrew.  LO, . Long-Term Memory in Stock Market Prices, Econometrica, , . , 1991 .

[34]  Christopher G. Lamoureux,et al.  Heteroskedasticity in Stock Return Data: Volume versus GARCH Effects , 1990 .

[35]  A. Lo.  Long-Term Memory in Stock Market Prices , 1989 .

[36]  R. Chou.  Volatility persistence and stock valuations: Some empirical evidence using garch , 1988 .

[37]  C. Gouriéroux,et al.  Hétérogénéité dans les modèles à représentation linéaire , 1988 .

[38]  R. Carroll,et al.  Variance Function Estimation , 1987 .

[39]  Stephen L Taylor,et al.  Modelling Financial Time Series , 1987 .

[40]  Alan G. White,et al.  The Pricing of Options on Assets with Stochastic Volatilities , 1987 .

[41]  Jonathan M. Karpoff.  The Relation between Price Changes and Trading Volume: A Survey , 1987, Journal of Financial and Quantitative Analysis.

[42]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[43]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[44]  J. Poterba,et al.  The Persistence of Volatility and Stock Market Fluctuations , 1984 .

[45]  S. Beckers,et al.  Variances of Security Price Returns Based on High , 1983 .

[46]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[47]  J. MacKinnon,et al.  Several Tests for Model Specication in the Pres-ence of Alternative Hypotheses , 1981 .

[48]  M. J. Klass,et al.  On the Estimation of Security Price Volatilities from Historical Data , 1980 .

[49]  M. Parkinson.  The Extreme Value Method for Estimating the Variance of the Rate of Return , 1980 .

[50]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[51]  B. Mandelbrot.  When Can Price Be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models , 1971 .

[52]  B. Mandelbrot.  The Variation of Certain Speculative Prices , 1963 .