Reviews of the subject
- Andersen, Torben and Luca Benzoni (2009) "Realized Volatility", edited by Andersen, T G, Richard A Davis, J P Kreiss and Thomas Mikosch in "Handbook of Financial Time Series", Springer-Verlag, 555-575
- Andersen, Torben, Tim Bollerslev and Francis X. Diebold (2009) "Parametric and nonparametric measurement of volatility," unpublished
- Barndorff-Nielsen, Ole E. and Neil Shephard (2007) " Variation, jumps and high frequency data in financial econometrics," edited by Blundell, R. and T. Persson and W. K. Newey in "Advances in Economics and Econometrics. Theory and Applications, Ninth World Congress," CUP, 328-372.
- McAleer, Michael and M.C. Medeiros (2008) "Realized volatility: a review," Econometric Reviews, 27, 10-45.
Has a long applied history. The econometrics of realized volatility (Rvol) was formalised by
- Andersen, Torben, Tim Bollerslev, Frank Diebold and Paul Labys (2001) "The distribution of exchange rate volatility", Journal of the American Statistical Association, 96, 42-55.
- Barndorff-Nielsen, Ole E. and Neil Shephard (2002) " Econometric analysis of realised volatility and its use in estimating stochastic volatility models", Journal of the Royal Statistical Society, Series B, 64, 253-280
Impact of noise on Rvol was formalised by
- Andersen, Torben G, Tim Bollerslev, Francis X Diebold and Paul Labys (2000), "Great realizations", Risk, 13, 105-108
- Bandi, Federico M. and Jeff R. Russell (2008) " Microstructure Noise, Realized Variance, and Optimal Sampling", Review of Economic Studies, 75, 339-369.
- Hansen, Peter R. and Asger Lunde (2006) " Realized variance and market microstructure noise (with discussion)", Journal of Business and Economic Statistics, 24, 127-218.
- Zhang, Lan, Per A. Mykland and Y. Ait-Sahalia (2005), "A tale of two time scales: determining integrated volatility with noisy high-frequency data", Journal of the American Statistical Assocation, 100, 1394-1411.
- Zhou , Bin (1996) "High-frequency data and volatility in foreign-exchange rates", Journal of Business and Economic Statistics, 14, 45-52
Various methods have been developed to mitigate the impact of noise. The library uses the realized kernel as that is what we know best.
- Barndorff-Nielsen, Ole E., Peter R. Hansen, Asger Lunde and Neil Shephard (2008) " Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise", Econometrica, 76, 1481-1536
- Barndorff-Nielsen, Ole E., Peter R. Hansen, Asger Lunde and Neil Shephard (2009a) "Realised kernels in Practice: trades and quotes", Econometrics Journal, forthcoming.
- Barndorff-Nielsen, Ole E., Peter R. Hansen, Asger Lunde and Neil Shephard (2009b) " Multivariate realised kernels: consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading", Unpublished paper: Oxford-Man Institute, University of Oxford
There are two other basic ways of reducing the impact of noise which have been formalised
- Zhang, Lan (2006) "Efficient estimation of stochastic volatility using noisy observations: a multi-scale approach", Bernoulli, 12, 1019-1043.
- Zhang, Lan, Per A Mykland and Yacine Ait-Sahalia (2005), "A tale of two time scales: determining integrated volatility with noisy high-frequency data", Journal of the American Statistical Association, 100, 1394-1411.
- Jacod, Jean, Y. Li, Per A. Mykland, Mark Podolskij and M. Vetter (2009) " Microstructure noise in the continuous case: the pre-averaging approach", Stochastic Processes and Their Applications, 119, 2249-2276.
Volatility forecasting using realized quantities
One of the most significant areas of use of realized measures is in forecast the volatility of financial assets. Here are some papers on this topics
- Andersen, Tim G, Tim Bollerslev, Francis X Diebold and Paul Labys (2001) " The distribution of exchange rate volatility", Journal of the American Statistical Association, 96, 42-55
- Andersen, Torben G, Tim Bollerslev, Francis X Diebold and Paul Labys (2003) "Modeling and Forecasting Realized Volatility", Econometrica, 71, 579-625
- Brownlees, Christian T. and G. M. Gallo (2006) "Financial econometrics at ultra-high frequency: data handling concerns", "Computational Statistics and Data Analysis", 51, 2232-2245
- Cipollini, F., Robert F Engle and G. Gallo (2007) "A model for multivariate non-negative valued processes in financial econometrics", unpublished paper, New York University
- Engle, Robert F. (2002) "New frontiers for ARCH models", Journal of Applied Econometrics, 17, 425-446
- Engle, Robert F. and G. Gallo (2006) " A Multiple Indicator Model for Volatility Using Intra Daily Data", Journal of Econometrics, 131, 3-27.
- Shephard, Neil and Kevin K. Shephard (2009) " Realising the future: forecasting with high frequency based volatility (HEAVY) models," Journal of Applied Econometrics, forthcoming.
Economic uses of realised volatility
A new research area is to explain excess returns by looking at volatility risk. The leading paper on this is
- Bollerslev, Tim, George Tauchen and Hao Zhou (2008) "Expected Stock Returns and Variance Risk Premia", Review of Financial Studies, forthcoming
Realised measures have allowed researchers to nonparametrically analyse jumps in financial data for the first time. The rests indicate there are many more jumps than had been previously thought. The early papers on this topic were
- Barndorff-Nielsen, Ole E and Neil Shephard (2004) "Power and bipower variation with stochastic volatility and jumps (with discussion)", Journal of Financial Econometrics, 2, 1-48.
- Barndorff-Nielsen, Ole E and Neil Shephard (2006) "Econometrics of testing for jumps in financial economics using bipower variation", Journal of Financial Econometrics, 4, 1-30.
- Mancini, C (2004) " Estimation of the characteristics of jump of a general Poisson-diffusion process", Scandinavian Actuarial Journal, 1, 42-52.
Other papers connected to realized measures
We are happy to add links to other papers on realized measures here, email one of the curators
- Ait-Sahalia, Yacine and Per A Mykland and Lan Zhang (2005) "How often to sample a continuous-time process in the presence of market microstructure noise", Review of Financial Studies,18, 351-416
- Ait-Sahalia, Yacine and Per A Mykland and Lan Zhang (2009) "Ultra high frequency volatility estimation with dependent microstructure noise", Journal of Econometrics, forthcoming.
- Andersen, T G, T Bollerslev and N Meddahi (2004) "Analytic Evaluation of Volatility Forecasts", IER, 45, 1079-1110.
- Andersen, T G, T Bollerslev and N Meddahi (2006) "Market Microstructure Noise and Realized Volatility Forecasting", Unpublished paper: Department of Economics, Duke University
- Bandi, Federico M and Jeffrey R Russell (2006) "Seperating microstructure noise from volatility", Journal of Financial Economics, 79, 655-692
- Barndorff-Nielsen, Ole E and Neil Shephard (2003) "Realised power variation and stochastic volatility", Bernoulli, 9, 243--265.
- Barndorff-Nielsen, Ole E and Neil Shephard (2004) "Econometric analysis of realised covariation: high frequency covariance, regression and correlation in financial economics", Econometrica, 72, 885-925.
- Barndorff-Nielsen, Ole E and Neil Shephard (2005) "Power variation and time change", Theory of Probability and Its Applications, 50, 1--15
- Barndorff-Nielsen, Ole E and Neil Shephard (2006) "Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes", Journal of Econometrics, 131, 217-252
- Barndorff-Nielsen, Ole E, Sven Eric Graversen, Jean Jacod and Neil Shephard (2006) "Limit theorems for realised bipower variation in econometrics", Econometric Theory, 677-719
- Barndorff-Nielsen, Ole E, Sylvia Kinnebrouck and Neil Shephard (2009) "Measuring downside risk: realised semivariance", in "Volatility and Time Series Econometrics: Essays in Honor of Robert F. Engle", edited by Bollerslev, Tim, Jeff Russell and Mark Watson, Oxford University Press, 117-136.
- Christensen, K, S Kinnevrock and M. Podolskij (2009) "Pre-averaging estimators of the ex-post covariance matrix," unpublished paper, CREATES, Aarhus University
- Delattre, S. and Jean Jacod (1997) "A central limit theorem for normalized functions of the increments of a diffusion process in the presence of round off errors", Bernoulli, 3, "1-28".
- Epps, T.W. (1979) "Comovements in stock prices in the very short run," Journal of the American Statistical Association, 74, 291-296.
- Fisher, L. (1966) "Some new stock-market indexes," Journal of Business, 39, 191-225.
- Fleming, J, C. Kirby amd B. Ostdiek (2003) "The economic values of volatility timing using realized volaitlity," Journal of Financial Economics, 67, 473-509.
- Ghysels, E, A.C. Harvey and E. Renault (1996) "Stochastic volatility," in C.R. Rao and G.S. Maddala (eds) "Statistical Methods in Finance," North-Holland, Amsterdam, 119-191.
- Gloter, A and J Jacod (2001a) "Diffusions with measurement errors. I --- local asymptotic normality", ESAIM: Probability and Statistics, 5, 225-242
- Gloter, A and J Jacod (2001b) "Diffusions with measurement errors. II --- measurement errors", ESAIM: Probability and Statistics, 5, 243--260
- Goncalves, S and Nour Meddahi (2004) "Bootstrapping realized volatility", Econometrica, 77, 283-306.
- Griffin, J.E. and R.C.A. Oomen (2006) "Covariance measurement in the presence of non-synchronous trading and market microstructure noise," Journal of Econometrics, forthcoming.
- Hansen, Peter K and G Horel ""Quadratic variation by Markov chains", unpublished paper, Department of Economics, Stanford University.
- Hansen, Peter K, Jeremy Large and Asger Lunde (2008) "Moving average estimators of integrated variance," Econometric Reviews, 27, 79-111.
- Hansen, Peter K and Asger Lunde (2005) "A realized variance for the whole day based on intermittent high-frequency data," Journal of Financial Econometrics, 3, 525-554.
- Hayashi, Takaki, J. Jacod and N. Yoshida (2008) "Irregularly sampling and central limit theorems for power variations: the continuous case," Unpublished paper, Keio University.
- Hayashi, Takaki and Nakahiro Yoshida (2005) "On covariance estimation of non-synchronously observed diffusion processes", Bernoulli, 11, 359-379.
- Jacod, J (1994) "Limit of random measures associated with the increments of a Brownian semimartingale", unpublished paper, Preprint number 120, Laboratoire de Probabilities, Universite Pierre et Marie Curie, Paris.
- Jacod, Jean (2008) "Asymptotic properties of realized power variations and related functionals of semimartingales", Stochastic Processes and Their Applications, 118, 517-559
- Jacod, Jean and Philip Protter (1998) "Asymptotic error distributions for the Euler method for stochastic differential equations", Annals of Probability, 26, 267--307.
- Kalnina, I and O. Linton (2008) "Estimating quadratic variation consistently in the presence of correlated measurement error," Journal of Econometrics, 147, 47-59.
- Kinnebrock, S. and Mark Podolskij (2008) "A note on the central limit theorem for bipower variation of general functions," Stochastic Processes and Their Applications, 118, 1056-1070.
- Lee, S and P A Mykland (2008) "Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics", Review of Financial Studies, 21, 2535-2563.
- Li, Yingying and Per Mykland (2007) "Are volatility estimators robust to modelling assumptions?", Bernoulli, 13, 601--622.
- Li, Y, P. Mykland, E. Renault, L. Zhang and X Zheng (2009) "Realized volatility when endogeniety of time matters," unpublished paper, Oxford-Man Institute
- Maheu, John M and Thomas H McCurdy (2002) "Nonlinear features of realised FX volatility", Review of Economics and Statistics, 84, 668-681.
- Maheu, John M and Thomas H McCurdy (2009) "Do high-frequency measures of volatility improve forecasts of return distributions?", Journal of Econometrics, forthcoming.
- Malliavin, P and M E Mancino (2002) "Fourier series method for measurement of multivariate volatilities", Finance and Stochastics, 6, 49--61
- Martens, M (2003) "Estimating unbiased and precise realized covariances," Unpublished paper: Department of Finance, Erasmus School of Economics.
- Meddahi, N (2002) "A theoretical comparison between integrated and realized volatilities", Journal of Applied Econometrics, 17, 479-508
- Mykland, Per A and L Zhang (2006) "ANOVA for diffusions and Ito processes, Annals of Statistics, 34, 1931-1963
- Mykland, Per A and L. Zhang (2009) "Inference for continuous semimartingales observed at high frequency: a general approach," Econometrica, 77, 1403-1445.
- Oomen, R A A (2005) "Properties of bias corrected realized variance in calender time and business time", Journal of Financial Econometrics, 3, 555-577
- Oomen, R A A (2006) "Properties of realized variance under alternative sampling schemes", Journal of Business and Economic Statistics, 24, 219-237
- Patton, Andrew J (2009) "Volatility Forecast Evaluation and Comparison Using Imperfect Volatility Proxies", Journal of Econometrics, forthcoming
- Phillips, Peter C.B. and Jun Yu (2008) "Information loss in volatility measurement with flat price trading," Unpublished paper: Cowles Foundation for Research in Economics, Yale University.
- Renault, E. and B. Werker (2008) "Causality effects in return volatility measurement with random times," unpublished paper, University of North Carolina
- Reno, R. (2003) "A closer look at the Epps effect," International journal of Theoretical and Applied Finance, 6, 87-102.
- Rosenberg, B (2005) "The behaviour of random variables with nonstationary variance and the distribution of security prices," in "Stochastic volatility: selected readings," edited by N. Shephard, Oxford University Press, 83-108. this was first circulated in an working paper series in 1972.
- Vetter, B. (2008) "Estimation methods in noisy diffusion models," Unpublished Ph.D. thesis, Institute of Mathematics, Ruhy University Bochum.
- Voev, V and A. Lunde (2007) "Integrated covariance estimation using high-frequency data in the presence of noise," Journal of Financial Econometrics, 5, 68-104.
- Zhang, L. (2009) "Estimating covariation: Epps effect and microstructure noise," Journal of Econometrics, forthcoming.
- Zhang, L, Per A Mykland and Yacine Ait-Sahalia (2009), "Edgeworth expansions for realized volatility and related estimators", Journal of Econometrics, forthcoming.
- Zhou, B (1998) "Parametric and nonparametric volatility measurement," in C.L. Dunis and B. Zhou (eds) "Nonlinear Modelling of High Frequency Financial Time Series," John Wiley and Sons Ltd, ch. 6, 109-123.