A Range-Based Test for the Parametric Form of the Volatility in Diffusion Models
We propose a new test for the parametric form of the volatility function in continuous time diffusion models of the type dXt = a(t,Xt)dt + s(t,Xt)dWt. Our approach involves a range-based estimation of the integrated volatility and the integrated quarticity, which are used to construct the test statistic. Under rather weak assumptions on the drift and volatility we prove weak convergence of the test statistic to a centered mixed Gaussian distribution. As a consequence we obtain a test, which is consistent for any fixed alternative. Moreover, we present a parametric bootstrap procedure which provides a better approximation of the distribution of the test statistic. Finally, it is demonstrated by means of Monte Carlo study that the range-based test is more powerful than the return-based test when comparing at the same sampling frequency.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Chan, K C, et al, 1992.
" An Empirical Comparison of Alternative Models of the Short-Term Interest Rate,"
Journal of Finance,
American Finance Association, vol. 47(3), pages 1209-1227, July.
- Tom Doan, "undated". "RATS programs to replicate CKLS(1992) estimation of interest rate models," Statistical Software Components RTZ00035, Boston College Department of Economics.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
- Ole BARNDORFF-NIELSEN & Svend Erik GRAVERSEN & Jean JACOD & Mark PODOLSKIJ & Neil SHEPHARD, 2004. "A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales," OFRC Working Papers Series 2004fe21, Oxford Financial Research Centre.
- Barndorff-Nielsen, Ole Eiler & Graversen, Svend Erik & Jacod, Jean & Podolskij, Mark, 2004. "A central limit theorem for realised power and bipower variations of continuous semimartingales," Technical Reports 2004,51, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
- Ole Barndorff-Nielsen & Svend Erik Graversen & Jean Jacod & Mark Podolskij & Neil Shephard, 2004. "A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales," Economics Papers 2004-W29, Economics Group, Nuffield College, University of Oxford.
- Asger Lunde & Peter Reinhard Hansen, 2004. "Realized Variance and IID Market Microstructure Noise," Econometric Society 2004 North American Summer Meetings 526, Econometric Society.
- Christensen, Kim & Podolskij, Mark, 2006. "Range-Based Estimation of Quadratic Variation," Technical Reports 2006,37, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
- Martens, Martin & van Dijk, Dick, 2007. "Measuring volatility with the realized range," Journal of Econometrics, Elsevier, vol. 138(1), pages 181-207, May.
- Martens, M.P.E. & van Dijk, D.J.C., 2006. "Measuring volatility with the realized range," Econometric Institute Research Papers EI 2006-10, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- Constantinides, George M, 1992. "A Theory of the Nominal Term Structure of Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 531-552.
- Christensen, Kim & Podolskij, Mark, 2007. "Realized range-based estimation of integrated variance," Journal of Econometrics, Elsevier, vol. 141(2), pages 323-349, December.
- Dette, Holger & Podolskij, Mark, 2008. "Testing the parametric form of the volatility in continuous time diffusion models--a stochastic process approach," Journal of Econometrics, Elsevier, vol. 143(1), pages 56-73, March.
- Holger Dette & Mark Podolskij & Mathias Vetter, 2006. "Estimation of Integrated Volatility in Continuous-Time Financial Models with Applications to Goodness-of-Fit Testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 259-278.
- Vetter, Mathias & Podolskij, Mark & Dette, Holger, 2004. "Estimation of integrated volatility in continuous time financial models with applications to goodness-of-fit testing," Technical Reports 2004,32, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
- Dette, Holger & Podolskij, Mark, 2005. "Testing the parametric form of the volatility in continuous time diffusion models: an empirical process approach," Technical Reports 2005,50, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
- John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:aah:create:2007-26. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.