ARMA representation of integrated and realized variances

Nour Meddahi Y

73 citations0/0 files storedEconometrics Journal

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Financial Risk and Volatility Modeling Stochastic processes and financial applications Market Dynamics and Volatility

Abstract

This paper derives the ARMA representation of integrated and realized variances when the spot variance depends linearly on two autoregressive factors, i.e. SR‐SARV(2) models. This class of processes includes affine, GARCH diffusion, and CEV models, as well as the eigenfunction stochastic volatility and the positive Ornstein–Uhlenbeck models. We also study the leverage effect case, and the relationship between the weak GARCH representation of returns and the ARMA representation of realized variances. Finally, various empirical implications of these ARMA representations are considered. We find that it is possible that some parameters of the ARMA representation are negative. Hence, the positiveness of the expected values of integrated or realized variances is not guaranteed. We also find that for some frequencies of observations, the continuous time model parameters may be weakly or not identified through the ARMA representation of realized variances.

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References

1986Generalized autoregressive conditional heteroskedasticity 1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1994Comparing Predictive Accuracy 2003Modeling and Forecasting Realized Volatility 1987The Pricing of Options on Assets with Stochastic Volatilities 1998Answering the Skeptics: Yes, Standard Volatility Models do Provide Accurate Forecasts 2001The distribution of realized stock return volatility 2002Econometric Analysis of Realized Volatility and its Use in Estimating Stochastic Volatility Models

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