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Jump-robust volatility estimation using nearest neighbor truncation. (English) Zbl 1443.62327

Summary: We propose two new jump-robust estimators of integrated variance that allow for an asymptotic limit theory in the presence of jumps. Specifically, our MedRV estimator has better efficiency properties than the tripower variation measure and displays better finite-sample robustness to jumps and small (“zero”) returns. We stress the benefits of local volatility measures using short return blocks, as this greatly alleviates the downward biases stemming from rapid fluctuations in volatility, including diurnal (intraday) U-shape patterns. An empirical investigation of the Dow Jones 30 stocks and extensive simulations corroborate the robustness and efficiency properties of our nearest neighbor truncation estimators.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
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[1] Aït-Sahalia, Y.; Jacod, J., Volatility estimators for discretely sampled Lévy processes, Annals of statistics, 35, 1, 355-392, (2007) · Zbl 1114.62109
[2] Aït-Sahalia, Y.; Mykland, P.A.; Zhang, L., Ultra high frequency volatility estimation with dependent microstructure noise, Journal of econometrics, 160, 190-203, (2011) · Zbl 1441.62577
[3] Andersen, T.G.; Bollerslev, T.; Diebold, F.X., Parametric and nonparametric volatility measurement, ()
[4] Andersen, T.G.; Bollerslev, T.; Diebold, F.X.; Labys, P., Great realizations, Risk magazine, 13, 105-108, (2000)
[5] Andersen, T.G.; Bollerslev, T.; Dobrev, D., No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects, jumps and i.i.d. noise: theory and testable distributional implications, Journal of econometrics, 138, 1, 125-180, (2007) · Zbl 1418.62371
[6] Andersen, T.G.; Bollerslev, T.; Meddahi, N., Correcting the errors: volatility forecast evaluation using high-frequency data and realized volatilities, Econometrica, 73, 1, 279-296, (2005) · Zbl 1152.91720
[7] Andersen, T.G., Dobrev, D.P., Schaumburg, E., 2008, Duration based volatility estimation, Manuscript, Northwestern University.
[8] Andersen, T.G., Dobrev, D.P., Schaumburg, E., Jun 2011, A functional filtering and neighborhood truncation approach to integrated quarticity estimation, NBER Working Paper (17152). · Zbl 1290.91186
[9] Bandi, F.M.; Russell, J.R., Volatility, ()
[10] Barndorff-Nielsen, O.E.; Graversen, S.E.; Jacod, J.; Podolskij, M.; Shephard, N., A central limit theorem for realized power and bipower variations of continuous semimartingales, () · Zbl 1106.60037
[11] Barndorff-Nielsen, O.E.; Graversen, S.E.; Jacod, J.; Shephard, N., Limit theorems for bipower variation in financial econometrics, Econometric theory, 22, 4, 677-719, (2006) · Zbl 1125.62114
[12] Barndorff-Nielsen, O.E.; Hansen, P.R.; Lunde, A.; Shephard, N., Realised kernels in practice: trades and quotes, Econometrics journal, 12, C1-C32, (2009) · Zbl 1179.91259
[13] Barndorff-Nielsen, O.E.; Shephard, N., Power and bipower variation with stochastic volatility and jumps, Journal of financial econometrics, 2, 1, 1-37, (2004) · Zbl 1095.60023
[14] Barndorff-Nielsen, O.E.; Shephard, N., Variation, jumps, market frictions and high frequency data in financial econometrics, () · Zbl 1095.60023
[15] Barndorff-Nielsen, O.E.; Shephard, N.; Winkel, M., Limit theorems for multipower variation in the presence of jumps, Stochastic processes and their applications, 116, 796-806, (2006) · Zbl 1096.60022
[16] Boudt, K., Croux, C., Laurent, S., 2008, Outlyingness weighted quadratic covariation, Working paper.
[17] Chaboud, A., Chiquoine, B., Hjalmarsson, E., Loretan, M., 2007, Frequency of observation and the estimation of integrated volatility in deep and liquid markets, Board of Governors of the Federal Reserve System, International Finance Discussion Papers.
[18] Christensen, K.; Oomen, R.; Podolskij, M., Realized quantile-based estimation of integrated variance, Journal of econometrics, 159, 74-98, (2010) · Zbl 1431.62473
[19] Christensen, K., Podolskij, M., 2007, Range-based estimation of quadratic variation, Working paper, Ruhr-Universität Bochum. · Zbl 1418.62294
[20] Corsi, F.; Pirino, D.; Renò, R., Threshold bipower variation and the impact of jumps on volatility forecasting, Journal of econometrics, 159, 276-288, (2010) · Zbl 1441.62656
[21] Dobrev, D., 2007, Capturing volatility from large price moves: generalized range theory and applications, Working paper, Northwestern University.
[22] Griffin, J.E.; Oomen, R.C., Sampling returns for realized variance calculations: tick time or transaction time?, Econometric reviews, 27, 230-253, (2008) · Zbl 1359.62514
[23] Hasbrouck, J., The dynamics of discrete bid and ask quotes, Journal of finance, 54, 6, 2109-2142, (1999)
[24] Hautsch, N., Podolskij, M., 2010, Pre-averaging based estimation of quadratic variation in the presence of noise and jumps: theory, implementation, and empirical evidence, Working paper, Humboldt University and ETH, Zurich.
[25] Huang, X.; Tauchen, G., The relative contribution of jumps to total price variance, Journal of financial econometrics, 3, 4, 456-499, (2005)
[26] Jacod, J.; Li, Y.; Mykland, P.; Podolskij, M.; Vetter, M., Mirostructure noise in the continuous case: the pre-averaging approach, Stochastic processes and their applications, 26, 2803-2831, (2009)
[27] Jacod, J.; Shiryaev, A.N., Limit theorems for stochastic processes, () · Zbl 0830.60025
[28] Lee, S.S.; Mykland, P.A., Jumps in financial markets: a new non-parametric test and jump dynamics, Review of financial studies, 21, 6, 2535-2563, (2008)
[29] Mancini, C., 2006, Estimating the integrated volatility in stochastic volatility models with Levy type jumps, Working paper, University of Firenze.
[30] McAleer, M.; Medeiros, M.C., Realized volatility: a review, Econometric reviews, 27, 1-3, 10-45, (2008) · Zbl 1148.62089
[31] Mykland, P.A., Renault, E., Zhang, L., 2008, Volatility estimation when trade times and returns are dependent, Working paper University of Chicago and UIC.
[32] Mykland, P.A.; Zhang, L., Inference for continuous semimartingales observed at high frequency, Econometrica, 77, 5, 1403-1445, (2009), URL http://econpapers.repec.org/RePEc:ecm:emetrp:v:77:y:2009:i:5:p:1403-1445 · Zbl 1182.62216
[33] Phillips, P.C., Yu, J., 2008, Information loss in volatility measurement with flat price trading, Working paper, Yale University and Singapore Management University.
[34] Podolskij, M.; Vetter, M., Estimation of volatility functionals in the simultaneous presence of microstructure noise and jumps, Bernoulli, 15, 634-658, (2009) · Zbl 1200.62131
[35] Revuz, D.; Yor, M., (), [u.a.]
[36] Veraart, A.E.D., 2008, Inference for the jump part of quadratic variation of itô semimartingales, Working paper, University of Aarhus.
[37] Zhang, L.; Mykland, P.A.; Aït-Sahalia, Y., A tale of two time scales: determining integrated volatility with noisy high-frequency data, Journal of the American statistical association, 100, 472, 1394-1411, (2005) · Zbl 1117.62461
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