Estimating quadratic variation using realized variance

By Ole E. Barndorff-Nielsen, N. Shephard. 2002

620 citations recorded by the source corpus.

This paper looks at some recent work on estimating quadratic variation using realised variance (RV) — that is sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high frequency financial return data. When the underlying process is a semimartingale we recall the fundamental result that RV is a consistent (as M →∞ ) estimator of quadratic variation (QV). We express concern that without additional assumptions it seems difficult to give any measure of uncertainty of the RV in this context. The position dramatically changes when we work with a rather general SV model — which is a special case of the semimartingale model. Then QV is integrated variance and we can derive the asymptotic distribution of the RV and its rate of convergence. These results do not require us to specify a model for either the drift or volatility functions, although we have to impose some weak regularity assumptions. We illustrate the use of the limit theory on some exchange rate data and some stock data. We show that even with large values of M the RV is sometimes a quite noisy estimator of integrated variance.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/838713dadf248f7b3488c0ce083f74f3e68d34e7

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Citations in the corpus

Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility (2007, positive): “However, as argued by Barndorff-Nielsen and Shephard (2002a) and Forsberg and Bollerslev (2002), the log-normal volatility distributions may be closely approximated by Inverse Gaussian distributions, which are formally closed under temporal aggregation.”
Volatility Forecast Evaluation and Comparison Using Imperfect Volatility Proxies (2005, neutral): “MAE : L ¡ σ(2)t , ht ¢ = ̄̄ σ(2)t − ht ̄̄ (10) MAE-SD : L ¡ σ(2)t , ht ¢ = ̄̄̄ σt − p ht ̄̄̄ (11)”
Econometric Analysis of Realised Covariation: High Frequency Covariance, Regression and Correlation in Financial Economics (2001, positive): “(38) The result on realised variances ∑M j=1 y 2 j(k) and ∑M j=1 y 2 j(l) were first derived in Barndorff-Nielsen and Shephard (2002a).”
The Volatility of Realized Volatility (2005, methodology): “In particular, Barndorff-Nielsen and Shephard (2002c) derive the approximate asymptotic distribution of the logarithmic transform of realized variance logRVt − log ∫ t t−1 2(s)ds√ 2Q ∗t M (RVt )2 d→ N (0, 1), Q ∗t ∈ (RQt ,RQQt ,RTQt) (16) Based on the realized quarticity measure, Barndorff-Nielsen…”
News - Good or Bad - and its Impact on Volatility Predictions over Multiple Horizons (2011, background): “Andersen, Bollerslev, and Diebold (2002), Andersen, Bollerslev, Diebold, and Labys (2003) and Barndorff-Nielsen and Shephard (2007) and references therein.”
A Discrete-Time Model for Daily S & P500 Returns and Realized Variations: Jumps and Leverage Effects (2009, positive): “Aburgeon literature dating back to Bollerslev (1987) and French et al.”
Measuring and modeling systematic risk in factor pricing models using high-frequency data (2003, methodology): “…but beyond the scope of the present paper, to formally assess the magnitude of the measurement errors in the present context (Bai et al., 2000; Barndorff-Nielson and Shephard, 2002a,b; Meddahi, 2002, all provide important theoretical results for the case of scalar realized volatility…”