Publication: A Fractionally Integrated Wishart Stochastic Volatility Model
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2013-01
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Abstract
There has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of the FIWSV model in order to obtain a closed form expression of moments. We conduct a two-step procedure, namely estimating the parameter of fractional integration via log-periodgram regression in the rst step, and estimating the remaining parameters via the generalized method of moments in the second step. Monte Carlo results for the procedure shows reasonable performances in nite samples. The empirical results for the bivariate data of the S&P 500 and FTSE 100 indexes show that the data favor the new FIWSV processes rather than one-factor and two-factor models of Wishart autoregressive processes for the covariance structure.
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The authors are most grateful to Yoshi Baba and Christian Hafner for very helpful comments and suggestions.
The 1rst author acknowledges the nancial support of the Japan Ministry of Education, Culture, Sports, Science
and Technology, Japan Society for the Promotion of Science, and Australian Academy of Science. The second author is most grateful for the nancial support of the Australian Research Council, National Science Council, Taiwan, and the Japan Society for the Promotion of Science. Address for correspondence: Faculty of Economics, Soka University, 1-236 Tangi-cho, Hachioji, Tokyo 192-8577, Japan.
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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.
Asai, M. and M. McAleer (2012), Leverage and Feedback Effects on Multifactor Wishart Stochastic Volatility for Option Pricing, Unpublished paper, Faculty of Economics, Soka University.
Asai, M., M. McAleer and M. Medeiros (2012), Asymmetry and Long Memory in Volatility Modeling, Journal of Financial Econometrics, 10, 495-512.
Asai, M., M. McAleer and J. Yu (2006), Multivariate Stochastic Volatility: A Review, Econometric Reviews, 25, 145-175.
Andrews, D.W.K. (1991), Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation, Econometrica 59, 817-858.
Baillie R.T., T. Bollerslev and H.O. Mikkelsen (1996), Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity, Journal of Econometrics, 74, 3-30.
Bauwens, L., S. Laurent, and J.V.K. Rombouts (2006), Multivariate GARCH: A Survey, Journal of Applied Econometrics, 21, 79-109.
Bellman, R. (1970). Introduction to Matrix Analysis, New York: McGraw-Hill.
Bollerslev, T. and H.O. Mikkelsen (1996), Modeling and Pricing Long-Memory in Stock Market Volatility, Journal of Econometrics, 73, 151-184.
Bollerslev, T., N. Sizova, and G. Tauchen (2011), Volatility in Equilibrium: Asymmetries and Dynamic Dependencies, Review of Finance, 16, 31-80.
Bollerslev, T. and H. Zhou (2002), Estimating Stochastic Volatility Diffusion Using Conditional Moments of Integrated Volatility, Journal of Econometrics, 109, 33-65.
Breidt, F.J., N. Crato and P. de Lima (1998), The Detection and Estimation of Long Memory, Journal of Econometrics, 83, 325-348.
Bru, M.-F. (1991), Wishart Processes, Journal of Theoretical Probability, 4, 725-751.
Caporin, M. and M. McAleer (2012), Do We Really Need Both BEKK and DCC? A Tale of Two Multivariate GARCH Models, Journal of Economic Surveys, 26, 736-751.
Chernov, M., A.R. Gallant, E. Ghysels, and G. Tauchen (2003), Alternative Models for Stock Price Dynamics, Journal of Econometrics, 116, 225-257.
Chib, S., Y. Omori and M. Asai (2009), Multivariate Stochastic Volatility, in: T.G. Andersen, R.A. Davis, J.-P. Kreiss and T. Mikosch (eds.), Handbook of Financial Time Series, Springer-Verlag, New York, 365-400.
Chiu, T.Y.M., T. Leonard, K.-W. Tsui (1996), The Matrix-Logarithmic Covariance Model, Journal of the American Statistical Association, 91, 198-210.
Comte, F. and E. Renault (1996), Long Memory Continuous Time Models, Journal of Econometrics, 73, 101-149.
Comte, F. and E. Renault (1998), Long Memory in Continuous-Time Stochastic Volatility Models, Mathematical Finance, 8, 291-323.
Dai, W. and C.C. Heyde (1996), Ito's Formula with Respect to Fractional Brownian Motion and Its Application, Journal of Applied Mathematics and Stochastic Analysis, 9, 439-448.
Deo, R.S. and C.M. Hurvich (2001), On the Log Periodogram Regression Estimator of the Memory Parameter in Long Memory Stochastic Volatility Models, Econometric Theory, 17, 686-710.
Ding, Z., C.W.J. Granger, and R. Engle (1993), A Long Memory Property of Stock Market Returns and a New Model, Journal of Empirical Finance, 1, 83-106.
Duffie, D., J. Pan, and K. Singleton (2000), Transform Analysis and Asset Pricing for Affine Jump Diffusions, Econometrica, 68, 1343-1376.
Fonseca, J., M. Grasselli, and C. Tebaldi (2008), A Multifactor Volatility Heston Model, Quantitative Finance, 8, 591-604.
Geweke, J. and S. Porter-Hudak (1983), The Estimation and Application of Long Memory Time Series Models, Journal of Time Series Analysis, 4, 221-238.
Gourieroux, C. (2006), Continuous Time Wishart Process for Stochastic Risk, Econometric Reviews, 25, 177-217.
Gourieroux, C. and R. Sufana (2010), Derivative Pricing with Wishart Multivariate Stochastic Volatility, Journal of Business & Economic Statistics, 28, 438-451.
Hansen, L.P. (1982), Large Sample Properties of Generalized Method of Moments Estimators, Econometrica, 50, 1029-1054.
Harvey, A.C. (1993), Long Memory in Stochastic Volatility, Unpublished Paper, London School of Economics.
Koopman, S.J., B. Jungbacker, and E. Hol (2005), Forecasting Daily Variability of the S&P 100 Stock Index Using Historical Realized and Implied Volatility Measurements, Journal of Empirical Finance, 12, 445-475.
McAleer, M., F. Chan, S. Hoti and O. Lieberman (2008), Generalized Autoregressive Conditional Correlation, Econometric Theory, 24, 1554-1583.
Mandelbrot, M.M and J.W. van Ness (1968), Fractional Brownian Motions, Fractional Noises and Applications, SIAM Review, 10, 422-437.
Muhle-Karbe, J., O. Pfaffel, and R. Stelzer (2012), Option Pricing in Multivariate Stochastic Volatility Models of OU Type, SIAM Journal on Financial Mathematics, 3, 66-94.
Newey, W.K., and K.D. West (1987), A Simple Positive Semi-De finite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix, Econometrica 55, 703-708.
Pong S., M.B. Shackelton, S.J. Taylor, and X. Xu (2004), Forecasting Currency Volatility: A Comparison of Implied Volatilities and AR(FI)MA Models, Journal of Banking and Finance, 28, 2541-2563.
Robinson, P.M. (1995), Log-Periodogram Regression of Time Series with Long Range Dependence, Annals of Statistics, 23, 1048-1072.
Robinson, P.M. (2005), Robust Covariance Matrix Estimation: HAC Estimates with Long Memory/Antipersistence Correction, Econometric Theory, 21, 171-180.