Corradi, Valentina and Distaso, Walter (2004) Testing for one-factor models versus stochastic volatility models. Working Paper. Coventry: Warwick Business School, Financial Econometrics Research Centre. (Working papers (Warwick Business School. Financial Econometrics Research Centre)).

Preview

PDF WRAP_Corradi_fwp04-18.pdf - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (817Kb)

Abstract

This paper proposes a testing procedure in order to distinguish between the case where the volatility of an asset price is a deterministic function of the price itself and the one where it is a function of one or more (possibly unobservable) factors, driven by not perfectly correlated Brownian motions. Broadly speaking, the objective of the paper is to distinguish between a generic one-factor model and a generic stochastic volatility model. In fact, no specific assumption on the functional form of the drift and variance terms is required. The proposed tests are based on the difference between two different nonparametric estimators of the integrated volatility process. Building on some recent work by Bandi and Phillips (2003) and Barndorff-Nielsen and Shephard (2004a), it is shown that the test statistics converge to a mixed normal distribution under the null hypothesis of a one factor diffusion process, while diverge in the case of multifactor models. The findings from a Monte Carlo experiment indicate that the suggested testing procedure has good finite sample properties.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	H Social Sciences > HG Finance H Social Sciences > HB Economic Theory
Divisions:	Faculty of Social Sciences > Warwick Business School > Financial Econometrics Research Centre Faculty of Social Sciences > Warwick Business School
Library of Congress Subject Headings (LCSH):	Accounting and price fluctuations, Stochastic analysis, Brownian movements, Distribution (Economic theory), Monte Carlo method
Series Name:	Working papers (Warwick Business School. Financial Econometrics Research Centre)
Publisher:	Warwick Business School, Financial Econometrics Research Centre
Place of Publication:	Coventry
Date:	November 2004
Number:	No.04-
Number of Pages:	38
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Economic and Social Research Council (Great Britain) (ESRC)
Grant number:	R000230006 (ESRC)
References:	Aït-Sahalia, Y. (1996). Testing Continuous Time Models of the Spot Interest Rate. Review of Financial Studies, 9, 385-426. Aït-Sahalia, Y., P.A. Mykland and L. Zhang (2003). How Often to Sample a Continuous Time Process in the Presence of Market Microstructure Noise. Review of Financial Studies, forthcoming. Andersen, T.G., T. Bollerslev and F.X. Diebold (2003). Some Like it Smooth and Some Like it Rough: Untangling Continuous and Jump Components in Measuring, Modelling and Forecasting Asset Return Volatility. Working Paper, Duke University. Andersen, T.G., T. Bollerslev, F.X. Diebold and H. Ebens (2001). The Distribution of Realized Stock Return Volatility. Journal of Financial Economics, 61, 43-76. Andersen, T.G., T. Bollerslev, F.X. Diebold and P. Labys (2001). The Distribution of Realized Exchange Rate Volatility. Journal of the American Statistical Association, 96, 42-55. Andersen, T.G., T. Bollerslev, F.X. Diebold and P. Labys (2003). Modelling and Forecasting Realized Volatility. Econometrica, 71, 579-625. Andersen, T.G., T. Bollerslev and N. Meddahi (2004a). Analytic Evaluation of Volatility Forecasts. International Economic Review, forthcoming. Andersen, T.G., T. Bollerslev and N. Meddahi (2004b). Correcting the Errors: Volatility Forecast Evaluation Using High Frequency Data and Realized Volatilities, Econometrica, forthcoming. Andersen, T.G. and J. Lund (1997). Estimating Continuous-Time Stochastic Volatility Models of the Short-Term Interest Rate. Journal of Econometrics, 77, 343-377. Awartani, B., V. Corradi and W. Distaso (2004). Testing and Modelling Market Microstructure Effects with an Application to the Dow Jones Industrial Average. Queen Mary, University of London. Bandi, F.M. (2002). Short Term Interest Rate Dynamics: A Spatial Approach. Journal of Financial Economics, 65, 73-110. Bandi, F.M. and G. Moloche (2001). On the Functional Estimation of Multivariate Diffusion Processes. MIT. Bandi, F.M. and P.C.B. Phillips (2001). A Simple Approach to the Parametric Estimation of Potentially Nonstationary Diffusions. Yale University. Bandi, F.M. and P.C.B. Phillips (2003). Fully Nonparametric Estimation of Scalar Diffusion Models. Econometrica, 71, 241-283. Bandi, F.M. and J.R. Russell (2003). Microstructure Noise, Realized Volatility, and Optimal Sampling. Working Paper, University of Chicago, Graduate School of Business. Barndorff-Nielsen, O.E., S.E. Graversen and N. Shephard (2004). Power Variation and Stochastic Volatility: A Review and Some New Results. Journal of Applied Probability, 41A, 133-143. Barndorff-Nielsen, O.E. and N. Shephard (2002). Econometric Analysis of Realized Volatility and Its Use in Estimating Stochastic Volatility Models. Journal of the Royal Statistical Society, Series B, 64, 253-280. Barndorff-Nielsen, O.E. and N. Shephard (2004a). A Feasible Central Limit Theory for Realized Volatility Under Leverage. Manuscript, Nuffield College, Oxford. Barndorff-Nielsen, O.E. and N. Shephard (2004b). Econometric Analysis of Realized Covariation: High Frequency Realized Covariance, Regression and Correlation in Financial Economics, Econometrica, 72, 885-925. Barndorff-Nielsen, O.E. and N. Shephard (2004c). Power and Bipower Variation with Stochastic Volatility and Jumps (with Discussion). Journal of Financial Econometrics, 2, 1-48. Barndorff-Nielsen, O.E. and N. Shephard (2004d). The Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation. Manuscript, Nuffield College, Oxford. Brennan, M.J. and E.S. Schwartz (1979). A Continuous Time Approach to the Pricing of Bonds. Journal of Banking and Finance, 3, 135-155. Chan, K.C., G.A. Karolyi, F.A. Longstaff and R.K. Sundaram (1992). An Empirical Comparison of Alternative Models of the Short-Term Interest Rate. Journal of Finance, 47, 1209-1227. Chernov, M., A.R. Gallant, E. Ghysels and G. Tauchen (2003). Alternative Models for Stock Price Dynamics. Journal of Econometrics, 116, 225-257. Chung, K.L. and R.J. Williams (1990). Introduction to Stochastic Integration. Birkhauser, Boston. Conley, T.G., E.G.J. Luttmer, L.P. Hansen and J.A. Scheinkman (1997). Short-Term Interest Rates as Subordinated Diffusions. Review of Financial Studies, 10, 525-577. Corradi, V. and W. Distaso (2004). Estimating and Testing Stochastic Volatility Models via Realized Measures. Manuscript, Queen Mary, University of London. Corradi, V. and H. White (1999). Specification Tests for the Variance of a Diffusion. Journal of Time Series Analysis, 20, 253-270. Cox, J.C., J.E. Ingersoll and S.A. Ross (1985). A Theory of the Term Structure of Interest Rates. Econometrica, 53, 385-407. Dai, Q. and K.J. Singleton (2000). Specification Analysis of Affine Term Structure Models. Journal of Finance, 55, 1943-1978. Dai, Q. and K.J. Singleton (2003). Expectation Puzzles, Time Varying Risk Premia, and Affine Models of the Term Structure. Journal of Financial Economics, 63, 415-441. Dette, H., M. Podolskij and M. Vetter (2004). Estimation of Integrated Volatility in Continuous Time Financial Models with Application to Goodness-of-Fit Testing. Manuscript, Ruhr-University, Bochum. Duffie, D. and K.J. Singleton (1997). An Econometric Model of the Term Structure of Interest-Rate Swap Yields. Journal of Finance, 52, 1287-1321. Durham, G.B. (2003). Likelihood-Based Specification Analysis of Continuous-Time Models of the Short-Term Interest Rate. Journal of Financial Economics, 70, 463-487. Fan, J. (2003). A Selective Overview of Nonparametric Methods in Financial Econometrics. Manuscript, Princeton University. Florens-Zmirou, D. (1993). On Estimating the Diffusion Coefficient from Discrete Observations. Journal of Applied Probability, 30, 790-804. Geman, D. and J. Horowitz (1980). Occupation Densities. Annals of Probability, 8, 1-67. Hansen, P.R. and A. Lunde (2004). An Unbiased Version of Realized Variance. Working Paper, Stanford University. Heston, S.L. (1993). A Closed Form Solution for Option with Stochastic Volatility with Applications to Bond and Currency Options. Review of Financial Studies, 6, 327-344. Huang, X. and G. Tauchen (2004). The Relative Contribution of Jumps to Total Price Variance. Duke University. Hull, J. and A. White (1987). The Pricing of Options on Assets with Stochastic Volatility. Journal of Finance, 42, 281-300. Hull, J. and A. White (1994). Numerical Procedures for Implementing Term Structure Models II: Two-Factor Models. Journal of Derivatives, 2, 37-48. Jacod, J. and P. Protter (1998). Asymptotic Error Distribution for the Euler Method for Stochastic Differential Equations. Annals of Probability, 26, 267-307. Jiang, G.J. (1998). Nonparametric Modelling of US Term Structure of Interest Rates and Implications on the Prices of Derivative Securities. Journal of Financial and Quantitative Analysis, 33, 465-497. Jiang, G.J. and J.L. Knight (1997). A Nonparametric Approach to the Estimation of Diffusion Processes, with an Application to a Short-Term Interest Rate Model. Econometric Theory, 13, 615-645. McKean, H. (1969). Stochastic Integrals. Academic Press, New York. Meddahi, N. (2001). An Eigenfunction Approach for Volatility Modeling, Manuscript, University of Montreal. Meddahi, N. (2002). A Theoretical Comparison between Integrated and Realized Volatility. Journal of Applied Econometrics, 17, 475-508. Meddahi, N. (2003). ARMA Representation of Integrated and Realized Variances. Econometrics Journal, 6, 334–355. Nelson, D.B. (1990). ARCH Models as Diffusion Approximations. Journal of Econometrics, 45, 7-38. Pardoux, E. and D. Talay (1985). Discretization and Simulation of Stochastic Differential Equations, Acta Applicandae Mathematicae, 3, 23-47. Pearson, N.D. and T.S. Sun (1994). Exploiting the Conditional Density in Estimating the Term Structure: An Application to the Cox, Ingersoll and Ross Model. Journal of Finance, 49, 1278-1304. Pritsker, M. (1998). Nonparametric Density Estimators and Tests of Continuous Time Interest Rate Models. Review of Financial Studies, 11, 449-487. Stanton, R. (1997). A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk. Journal of Finance, 52, 1973-2002. Vasicek, O.A. (1977). An Equilibrium Characterization of the Term Structure. Journal of Financial Economics, 5, 177-188. Wiggings, J.B. (1987). Options Values under Stochastic Volatility: Theory and Empirical Estimates. Journal of Financial Economics, 10, 351-372. Zhang, L., P.A. Mykland and Y. Aït-Sahalia (2003). A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data. Working Paper, Carnegie Mellon University.
URI:	http://wrap.warwick.ac.uk/id/eprint/1782

Request changes to a record

Actions (login required)

View Item