Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-24T20:57:04.270Z Has data issue: false hasContentIssue false

Basis Convergence and Long Memory in Volatility When Dynamic Hedging with Futures

Published online by Cambridge University Press:  06 April 2009

Abstract

When market returns follow a long memory volatility process, standard approaches to estimating dynamic minimum variance hedge ratios (MVHRs) are misspecified. Simulation results and an application to the S&P 500 index document the magnitude of the misspecification that results from failure to account for basis convergence and long memory in volatility. These results have important implications for the estimation of MVHRs in the S&P 500 example and other markets as well.

Type
Research Article
Copyright
Copyright © School of Business Administration, University of Washington 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Andersen, T., and Bollerslev, T.. “Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High-Frequency Returns.” Journal of Finance, 52 (1997a), 975–1005.Google Scholar
Andersen, T., and Bollerslev, T.. “Intraday Periodicity and Volatility Persistence in Financial Markets.” Journal of Empirical Finance, 4 (1997b), 115–158.CrossRefGoogle Scholar
Andersen, T., and Bollerslev, T.. “Deutsche Mark-Dollar Volatility: Intraday Activity Patterns, Macroeconomic Announcements and Longer-Run Dependencies.” Journal of Finance, 53 (1998), 219–265.CrossRefGoogle Scholar
Baillie, R.; Bollerslev, T.; and Mikkelsen, H.. “Fractionally Integrated Generalized Autoregressive Conditional Heteroscedasticity.” Journal of Econometrics, 74 (1996), 3–30.CrossRefGoogle Scholar
Bollerslev, T.; Engle, R.; and Wooldridge, J.. “A Capital Asset Pricing Model with Time-Varying Covariances.” Journal of Political Economy, 96 (1988), 116–131.CrossRefGoogle Scholar
Bollerslev, T., and Mikkelsen, H.. “Modelling and Pricing Long Memory in Stock Market Volatility.” Journal of Econometrics, 73 (1996), 151–184.CrossRefGoogle Scholar
Breidt, F.; Crato, N.; and Lima, P. de. “The Detection and Estimation of Long Memory in Stochastic Volatility.”. Journal of Econometrics, 83 (1998), 325–348.CrossRefGoogle Scholar
Breidt, F., and Hsu, N.. “A Class of Nearly Long-Memory Time Series Models.” International Journal of Forecasting, 18 (2002), 265–281.CrossRefGoogle Scholar
Brennan, M., and Schwartz, E.. “Arbitrage in Stock Index Futures.” Journal of Business, 63 (1990), 7–31.Google Scholar
Brunetti, C., and Gilbert, C.. “Bivariate FIGARCH and Fractional Cointegration.” Journal of Empirical Finance, 7 (2000), 509–530.CrossRefGoogle Scholar
Buhler, W., and Kempf, A.. “DAX Index Futures: Mispricing and Arbitrage in German Markets.” Journal of Futures Markets, 15 (1995), 833–859.CrossRefGoogle Scholar
Castelino, M.Basis Volatility: Implications for Hedging.” Journal of Financial Research, 12 (1989), 157–172.CrossRefGoogle Scholar
Castelino, M.Minimum-Variance Hedging with Futures Revisited.” Journal of Portfolio Management, 16 (1990a), 74–80.CrossRefGoogle Scholar
Castelino, M.Futures Markets and Hedging: The Time Dimension.” Journal of Quantitative Economics, 6 (1990b), 271–287.Google Scholar
Castelino, M.Hedge Effectiveness: Basis Risk and Minimum-Variance Hedging.” Journal of Futures Markets, 12 (1992), 187–201.CrossRefGoogle Scholar
Castelino, M., and Francis, J.. “Basis Speculation in Commodity Futures: The Maturity Effect.” Journal of Futures Markets, 2 (1982), 195–207.CrossRefGoogle Scholar
Cecchetti, S.; Cumby, R.; and Figlewski, S.. “Estimation of the Optimal Futures Hedge.” Review of Economics and Statistics, 70 (1988), 623–630.CrossRefGoogle Scholar
Chen, S.; Lee, C.; and Shrestha, K.. “Futures Hedge Ratios: A Review.” Quarterly Review of Economics and Finance, 43 (2003), 433–465.CrossRefGoogle Scholar
Chen, Y.; Duan, J.; and Hung, M.. “Volatility and Maturity Effects in the Nikkei Index Futures.” Journal of Futures Markets, 19 (1999), 895–909.3.0.CO;2-C>CrossRefGoogle Scholar
Dacorogna, M.; Muller, U.; Nagler, R.; Olsen, R.; and Pictet, O.. “A Geographical Model for the Daily and Weekly Seasonal Volatility in the Foreign Exchange Market.” Journal of International Money and Finance, 12 (1993), 413–438.CrossRefGoogle Scholar
Davidson, J.Moment and Memory Properties of Linear Conditional Heteroscedasticity Models and a New Model.” Journal of Business and Economic Statistics, 22 (2004), 16–29.CrossRefGoogle Scholar
Diebold, F., and Inoue, A.. “Long Memory and Regime Switching.” Journal of Econometrics, 105 (2001), 131–159.CrossRefGoogle Scholar
Ding, Z., and Granger, C.. “Modelling Volatility Persistence of Speculative Returns: A New Approach.” Journal of Econometrics, 73 (1996), 185–215.CrossRefGoogle Scholar
Ding, Z.; Granger, C.; and Engle, R.. “A Long Memory Property of Stock Market Returns and a New Model.” Journal of Empirical Finance, 1 (1993), 83–106.CrossRefGoogle Scholar
Ederington, L.The Hedging Performance of the New Futures Markets.” Journal of Finance, 34 (1979), 157–170.CrossRefGoogle Scholar
Engle, R., and Ng, V.. “Measuring and Testing the Impact of News on Volatility.” Journal of Finance, 48 (1993), 1749–1778.CrossRefGoogle Scholar
Figlewski, S.Hedging with Financial Futures for Institutional Investors: From Theory to Practice. Cambridge, MA: Ballinger (1986).Google Scholar
Ghosh, A.Hedging with Stock Index Futures: Estimation and Forecasting with Error Correction Model.” Journal of Futures Markets, 13 (1993), 743–752.CrossRefGoogle Scholar
Granger, C.Long Memory Relationships and the Aggregation of Dynamic Models.” Journal of Econometrics, 14 (1980), 227–238.CrossRefGoogle Scholar
Granger, C., and Hyung, N.. “Occasional Structural Breaks and Long Memory with an Application to the S&P 500 Absolute Stock Returns.” Journal of Empirical Finance, 11 (2004), 399–421.CrossRefGoogle Scholar
Hsu, C.Change Point Estimation in Regression with I(d) Variables.” Economics Letters, 70 (2001), 147–155.CrossRefGoogle Scholar
Hyung, N., and Franses, P.. “Structural Breaks and Long Memory in US Inflation Rates: Do They Matter for Forecasting?” Working Paper, Econometric Institute Research Report EI2001–13 (2001).Google Scholar
Karagozoglu, A.; Martell, T.; and Wang, G.. “The Split of the S&P 500 Futures Contract: Effects on Liquidity and Market Dynamics.” Review of Quantitative Finance and Accounting, 21 (2003), 323–348.CrossRefGoogle Scholar
Kirman, A., and Teyssiere, G.. “Microeconomic Models for Long Memory in the Volatility of Financial Time Series.” Studies in Nonlinear Dynamics and Econometrics, 5 (2002a), 281–302.Google Scholar
Kirman, A., and Teyssiere, G.. “Bubbles and Long-Range Dependence in Asset Prices Volatilities.” In Equilibrium, Markets and Dynamics, Hommes, C., Ramer, R. and Withagen, C., eds. New York: Springer Verlag (2002b).Google Scholar
Koutmos, G., and Pericli, A.. “Dynamic Hedging of Commercial Paper with T-Bill Futures.” Journal of Futures Markets, 18 (1998), 925–938.3.0.CO;2-K>CrossRefGoogle Scholar
Kroner, K., and Sultan, J.. “Time-Varying Distributions and Dynamic Hedging with Foreign Currency Futures.” Journal of Financial and Quantitative Analysis, 28 (1993), 535–551.CrossRefGoogle Scholar
Lee, G.Contemporary and Long-Run Correlations: A Covariance Component Model and Studies on the S&P 500 Cash and Futures Markets.” Journal of Futures Markets, 19 (1999), 877–894.3.0.CO;2-B>CrossRefGoogle Scholar
Lien, D.The Effect of the Cointegration Relationship on Futures Hedging: A Note.” Journal of Futures Markets, 16 (1996), 773–780.3.0.CO;2-L>CrossRefGoogle Scholar
Lien, D., and Luo, X.. “Multiperiod Hedging in the Presence of Conditional Heteroscedasticity.” Journal of Futures Markets, 14 (1994), 927–955.CrossRefGoogle Scholar
Lien, D., and Tse, Y.. “Fractional Cointegration and Futures Hedging.” Journal of Futures Markets, 19 (1999), 457–474.3.0.CO;2-U>CrossRefGoogle Scholar
Lim, K.Arbitrage and Price Behavior of the Nikkei Stock Index Futures.” Journal of Futures Markets, 12 (1992), 151–161.CrossRefGoogle Scholar
Liu, M.Modelling Long Memory in Stock Market Volatility.” Journal of Econometrics, 99 (2000), 139–171.CrossRefGoogle Scholar
Lobato, I., and Savin, N.. “Real and Spurious Long-Memory Properties of Stock Market Data.” Journal of Business and Economic Statistics, 16 (1998), 261–283.Google Scholar
Morana, C., and Beltratti, A.. “Structural Change and Long-Range Dependence in Volatility of Exchange Rates: Either, Neither or Both?Journal of Empirical Finance, 11, (2004), 629–658.CrossRefGoogle Scholar
Muller, U.; Dacorogna, M.; Dave, R.; Olsen, R.; Pictet, O.; and Weizsacker, J.. “Volatilities of Different Time Resolutions-Analyzing the Dynamics of Market Components.” Journal of Empirical Finance, 4 (1997), 213–239.CrossRefGoogle Scholar
Nyblom, J.Testing for the Constancy of Parameters over Time.” Journal of the American Statistical Association, 84 (1989), 223–230.CrossRefGoogle Scholar
Pafka, S., and Matyas, L.. “Multivariate Diagonal FIGARCH: Specification, Estimation and Application to Modelling Exchange Rates Volatility.” Working Paper No. 5/2001, CEU Department of Economics (2001).Google Scholar
Park, T., and Switzer, L.. “Bivariate GARCH Estimation of the Optimal Hedge Ratios for Stock Index Futures: A Note.” Journal of Futures Markets, 15 (1995), 61–67.CrossRefGoogle Scholar
Silberberg, G., and Pafka, S.. “A Sufficient Condition for the Positive Definiteness of the Covariance Matrix of a Multivariate GARCH Model.” Working Paper No. 7/2001, CEU Department of Economics (2001).CrossRefGoogle Scholar
Sim, A., and Zurbruegg, R.. “The KOSPI 200 and Dynamic Hedging Effectiveness During the Asian Financial Crisis.” Working Paper, University of New South Wales (2000).Google Scholar
Teyssiere, G.Modelling Exchange Rates Volatility with Multivariate Long-Memory ARCH Processes.” Working Paper GREQAM DT 97B03, Marseille, France (1997).Google Scholar
Teyssiere, G. “Multivariate Long-Memory ARCH Modelling for High-Frequency Foreign Exchange Rates.” Proceedings of the High-Frequency Data in Finance II Conference, Zurich: Olsen and Associates (1998).Google Scholar
Tse, Y.The Conditional Heteroscedasticity of the Yen-Dollar Exchange Rate.” Journal of Applied Econometrics, 13 (1998), 49–55.3.0.CO;2-O>CrossRefGoogle Scholar
Tse, Y., and Tsui, A.. “A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations.” Journal of Business and Economic Statistics, 20 (2002), 351–362.CrossRefGoogle Scholar
Twite, G.The Pricing of Australian Index Futures Contracts with Taxes and Transaction Costs.”Australian Journal of Management, 23 (1998), 57–81.CrossRefGoogle Scholar
Working, H.Futures Trading and Hedging.” American Economic Review, 43 (1953a), 314–343.Google Scholar
Working, H.Hedging Reconsidered.” Journal of Farm Economics, 35 (1953b), 544–561.CrossRefGoogle Scholar
Working, H.New Concepts Concerning Futures Markets and Prices.” American Economic Review, 51 (1961), 431–459.Google Scholar