Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Short Term Load Forecasting in the Industry for Establishing Consumption Baselines: A French Case Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Spot Volatility Estimation for High-Frequency Data: Adaptive Estimation in Practice

Authors : Till Sabel, Johannes Schmidt-Hieber, Axel Munk

Published in: Modeling and Stochastic Learning for Forecasting in High Dimensions

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We develop further the spot volatility estimator introduced in Hoffmann et al. (Ann Inst H Poincaré (B) Probab Stat 48(4):1186–1216, 2012) from a practical point of view and make it applicable to the analysis of high-frequency financial data. In a first part, we adjust the estimator substantially in order to achieve good finite sample performance and to overcome difficulties arising from violations of the additive microstructure noise model (e.g. jumps, rounding errors). These modifications are justified by simulations. The second part is devoted to investigate the behavior of volatility in response to macroeconomic events. We give evidence that the spot volatility of Euro-BUND futures is considerably higher during press conferences of the European Central Bank. As an outlook, we present an estimator for the spot covolatility of two different prices.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Massive-Scale Simulation of Electrical Load in Smart Grids Using Generalized Additive Models
next chapter Time Series Prediction via Aggregation: An Oracle Bound Including Numerical Cost
Appendix
Available only for authorised users
Literature
1.
2.
Ait-Sahalia, Y., & Yu, J. (2009). High frequency market microstructure noise estimates and liquidity measures. The Annals of Applied Statistics, 3, 422–457.MATHMathSciNetCrossRef
3.
Ait-Sahalia, Y., Mykland, P. A., & Zhang, L. (2005). How often to sample a continuous-time process in the presence of market microstructure noise. The Review of Financial Studies, 18, 351–416.CrossRef
4.
Ait-Sahalia, Y., Fan, J., & Xiu, D. (2010). High-frequency covariance estimates with noisy and asynchronous financial data. Journal of the American Statistical Association, 105, 1504–1517.MathSciNetCrossRef
5.
Ait-Sahalia, Y., Jacod, J., & Li, J. (2012). Testing for jumps in noisy high frequency data. Journal of Econometrics, 168, 207–222.MathSciNetCrossRef
6.
Andersen, T. G., & Bollerslev, T. (1998). Deutsche Mark-Dollar volatility: Intraday activity patterns, macroeconomic announcements, and longer run dependencies. The Journal of Finance, 53, 219–265.CrossRef
7.
Autin, F., Freyermuth, J. M., & von Sachs, R. (2011). Ideal denoising within a family of tree-structured wavelet estimators. The Electronic Journal of Statistics, 5, 829–855.MATHCrossRef
8.
Bandi, F., & Russell, J. (2008). Microstructure noise, realized variance, and optimal sampling. The Review of Economic Studies, 75, 339–369.MATHMathSciNetCrossRef
9.
Barndorff-Nielsen, O. E., Hansen, P. R., Lunde, A., & Stephard, N. (2008). Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise. Econometrica, 76(6), 1481–1536.MATHMathSciNetCrossRef
10.
Barndorff-Nielsen, O. E., Hansen, P. R., Lunde, A., & Shephard, N. (2011). Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading. Journal of Econometrics, 162, 149–169.MathSciNetCrossRef
11.
Bibinger, M. (2011). Efficient covariance estimation for asynchronous noisy high-frequency data. Scandinavian Journal of Statistics, 38, 23–45.MATHMathSciNetCrossRef
12.
13.
Cai, T., & Wang, L. (2008). Adaptive variance function estimation in heteroscedastic nonparametric regression. The Annals of Statistics, 36, 2025–2054.MATHMathSciNetCrossRef
14.
Cai, T., & Zhou, H. (2009). A data-driven block thresholding approach to wavelet estimation. The Annals of Statistics, 37, 569–595.MATHMathSciNetCrossRef
15.
Cai, T., Munk, A., & Schmidt-Hieber, J. (2010). Sharp minimax estimation of the variance of Brownian motion corrupted with Gaussian noise. Statistica Sinica, 20, 1011–1024.MATHMathSciNet
16.
Carr, P., & Wu, L. (2004). Time-changed Lévy processes and option pricing. Journal of Financial Economics, 71(1), 113–141.CrossRef
17.
Christensen, K., Kinnebrock, S., & Podolskij, M. (2010). Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data. Journal of Econometrics, 159, 116–133.MathSciNetCrossRef
18.
Cohen, A. (2003). Numerical analysis of wavelet methods. Amsterdam/Boston: Elsevier.MATH
19.
Cohen, A., Daubechies, I., & Vial, P. (1993). Wavelets on the interval and fast wavelet transforms. Applied and Computational Harmonic Analysis, 1, 54–81.MATHMathSciNetCrossRef
20.
Cont, R., & Tankov, P. (2004). Financial modelling with jump processes. Boca Raton: CRC Press.MATH
21.
Dahlhaus, R., & Neddermeyer, J. C. (2013). On-line spot volatility-estimation and decomposition with nonlinear market microstructure noise models. ArXiv e-prints. arXiv:1006.1860v4.
22.
23.
Delbaen, F., & Schachermayer, W. (1994). A general version of the fundamental theorem of asset pricing. Mathematische Annalen, 300, 463–520.MATHMathSciNetCrossRef
24.
Delbaen, F., & Schachermayer, W. (1998). The fundamental theorem of asset pricing for unbounded stochastic processes. Mathematische Annalen, 312, 215–250.MATHMathSciNetCrossRef
25.
26.
Donoho, D., Johnstone, I. M., Kerkyacharian, G., & Picard, D. (1995). Wavelet shrinkage: Asymptopia? Journal of the Royal Statistical Society: Series B Statistical Methodology, 57, 301–369.MATHMathSciNet
27.
Dorfleitner, G. (2004). How short-termed is the trading behaviour in Eurex futures markets? Applied Financial Economics, 14, 1269–1279.CrossRef
28.
Ederington, L. H., & Lee, J. H. (1993). How markets process information: New releases and volatility. The Journal of Finance, 48, 1161–1191.CrossRef
29.
Ederington, L. H., & Lee, J. H. (1995). The short-run dynamics of the price adjustment to new information. Journal of Financial and Quantitative Analysis, 30, 117–134.CrossRef
30.
Fan, J., & Wang, Y. (2007). Multi-scale jump and volatility analysis for high-frequency financial data. Journal of the American Statistical Association, 102, 1349–1362.MATHMathSciNetCrossRef
31.
32.
Gloter, A., & Jacod, J. (2001). Diffusions with measurement errors. I. Local asymptotic normality. ESAIM Probability and Statistics, 5, 225–242.
33.
Gloter, A., & Jacod, J. (2001). Diffusions with measurement errors. II. Optimal estimators. ESAIM Probability and Statistics, 5, 243–260.
34.
Hasbrouck, J. (1993). Assessing the quality of a security market: A new approach to transaction-cost measurement. The Review of Financial Studies, 6, 191–212.CrossRef
35.
Hautsch, N., & Podolskij, M. (2013). Pre-averaging based estimation of quadratic variation in the presence of noise and jumps: Theory, implementation, and empirical evidence. Journal of Business and Economic Statistics, 31(2), 165–183.MathSciNetCrossRef
36.
Hayashi, T., & Yoshida, N. (2005). On covariance estimation of non-synchronously observed diffusion processes. Bernoulli, 11, 359–379.MATHMathSciNetCrossRef
37.
Hoffmann, M., Munk, A., & Schmidt-Hieber, J. (2012). Adaptive wavelet estimation of the diffusion coefficient under additive error measurements. Annales de l’Institut Henri Poincaré (B) Probabilités et Statistiques, 48(4), 1186–1216.MATHMathSciNetCrossRef
38.
Jacod, J., Li, Y., Mykland, P. A., Podolskij, M., & Vetter, M. (2009). Microstructure noise in the continuous case: The pre-averaging approach. Stochastic Processes and Their Applications, 119(7), 2249–2276.MATHMathSciNetCrossRef
39.
Jansen, D., & de Haan, J. (2006). Look who’s talking: ECB communication during the first years of EMU. International Journal of Finance and Economics, 11, 219–228.CrossRef
40.
Li, W. V., & Shao, Q. M. (2002). A normal comparison inequality and its applications. Probability Theory and Related Fields, 122, 494–508.MATHMathSciNetCrossRef
41.
Li, Y., Zhang, Z., & Zheng, X. (2013). Volatility inference in the presence of both endogenous time and microstructure noise. Stochastic Processes and Their Applications, 123, 2696–2727.MATHMathSciNetCrossRef
42.
Lunde, A., & Zebedee, A. A. (2009). Intraday volatility responses to monetary policy events. Financial Markets and Portfolio Management, 23(4), 383–299.CrossRef
43.
Madahavan, A. (2000). Market microstructure: A survey. Journal of Financial Markets, 3, 205–258.CrossRef
44.
Munk, A., & Schmidt-Hieber, J. (2010). Nonparametric estimation of the volatility function in a high-frequency model corrupted by noise. The Electronic Journal of Statistics, 4, 781–821.MATHMathSciNetCrossRef
45.
Munk, A., & Schmidt-Hieber, J. (2010). Lower bounds for volatility estimation in microstructure noise models. In J.O. Berger, T.T. Cai, & I.M. Johnstone (Eds.) Borrowing strength: Theory powering applications - a festschrift for Lawrence D. Brown (Vol. 6, pp. 43–55). Beachwood: Institute of Mathematical Statistics
46.
Podolskij, M., & Vetter, M. (2009). Estimation of volatility functionals in the simultaneous presence of microstructure noise and jumps. Bernoulli, 15, 634–658.MATHMathSciNetCrossRef
47.
Reiß, M. (2011). Asymptotic equivalence for inference on the volatility from noisy observations. The Annals of Statistics, 39(2), 772–802.MATHMathSciNetCrossRef
48.
Schmidt-Hieber, J. (2010). Nonparametric methods in spot volatility estimation. PhD thesis, Georg-August-Universität Göttingen.
49.
van der Ploeg, A. (2005). Stochastic volatility and the pricing of financial derivatives (n∘366 of the Tinbergen Institute research series, No. 366).
50.
Veraart, A. E., & Winkel, M. (2010). Time change. In R. Cont (Ed.), Encyclopedia of quantitative finance (pp. 1812–1816). Chichester: Wiley.
51.
Wassermann, L. (2010). All of nonparametric statistics (Springer texts in statistics). New York/London: Springer.
52.
Zhang, L. (2006). Efficient estimation of stochastic volatility using noisy observations: A multi-scale approach. Bernoulli, 12, 1019–1043.MATHMathSciNetCrossRef
53.
Zhang, L. (2011). Estimating covariation: Epps effect and microstructure noise. Journal of Econometrics, 160, 33–47.MathSciNetCrossRef
54.
Zhang, L., Mykland, P., & Ait-Sahalia, Y. (2005). A tale of two time scales: Determining integrated volatility with noisy high-frequency data. Journal of the American Statistical Association, 472, 1394–1411.MathSciNetCrossRef
55.
Zhou, B. (1996). High-frequency data and volatility in foreign-exchange rates. Journal of Business and Economic Statistics, 14, 45–52.
Metadata
Title
Spot Volatility Estimation for High-Frequency Data: Adaptive Estimation in Practice
Authors
Till Sabel
Johannes Schmidt-Hieber
Axel Munk
Copyright Year
2015
Book
Modeling and Stochastic Learning for Forecasting in High Dimensions

Print ISBN: 978-3-319-18731-0

Electronic ISBN: 978-3-319-18732-7

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-18732-7_12

Premium Partner

    Image Credits