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Forecasting Volatility Using Long Memory and Comovements: An Application to Option Valuation under SFAS 123R

Published online by Cambridge University Press:  19 February 2010

George J. Jiang  and
Yisong S. Tian
George J. Jiang
Affiliation:
Eller College of Management, University of Arizona, PO Box 210108, Tucson, AZ 85721. gjiang@eller.arizona.edu
Yisong S. Tian
Affiliation:
Schulich School of Business, York University, 4700 Keele St., Toronto, ON, M3J 1P3, Canada. ytian@ssb.yorku.ca
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Abstract

Horizon-matched historical volatility is commonly used to forecast future volatility for option valuation under the Statement of Financial Accounting Standards (SFAS) 123R. In this paper, we empirically investigate the performance of using historical volatility to forecast long-term stock return volatility in comparison with a number of alternative forecasting methods. In analyzing forecasting errors and their impact on reported income due to option expensing, we find that historical volatility is a poor forecast for long-term volatility and that shrinkage adjustment toward comparable-firm volatility only slightly improves its performance. Forecasting performance can be improved substantially by incorporating both long memory and comovements with common market factors. We also experiment with a simple mixed-horizon realized volatility model and find its long-term forecasting performance to be more accurate than historical forecasts but less accurate than long-memory forecasts.

Type
Research Articles
Information
Journal of Financial and Quantitative Analysis , Volume 45 , Issue 2 , April 2010 , pp. 503 - 533
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2010

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References

Aboody, D.; Barth, M. E.; and Kasznik, R.. “Do Firms Understate Stock Option-Based Compensation Expense Disclosed under SFAS 123?” Review of Accounting Studies, 11 (2006), 429–461.Google Scholar
Alford, A. W., and Boatsman, J. R.. “Predicting Long-Term Stock Return Volatility: Implications for Accounting and Valuation of Equity Derivatives.” Accounting Review, 70 (1995), 599–618.Google Scholar
Andersen, T. G.; Bollerslev, T.; Christoffersen, P. F.; and Diebold, F. X.. “Volatility and Correlation Forecasting.” In Handbook of Economic Forecasting, 1, Elliot, G., Granger, C. W. J., and Timmermann, A., eds. Amsterdam: North Holland (2006), 777–878.Google Scholar
Andersen, T. G.; Bollerslev, T.; Diebold, F. X.; and Ebens, H.. “The Distribution of Realized Stock Return Volatility.” Journal of Financial Economics, 61 (2001), 43–76.Google Scholar
Andersen, T. G.; Bollerslev, T.; Diebold, F. X.; and Labys, P.. “The Distribution of Realized Exchange Rate Volatility.” Journal of the American Statistical Association, 96 (2001), 42–55.CrossRefGoogle Scholar
Andersen, T. G.; Bollerslev, T.; Diebold, F. X.; and Labys, P.. “Modeling and Forecasting Realized Volatility.” Econometrica, 71 (2003), 579–625.Google Scholar
Baillie, R. T.; Bollerslev, T.; and Mikkelsen, H. O.. “Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity.” Journal of Econometrics, 74 (1996), 3–30.Google Scholar
Balsam, S.; Mozes, H. A.; and Newman, H. A.. “Managing Pro Forma Stock Option Expense under SFAS No. 123.” Accounting Horizons, 17 (2003), 31–45.Google Scholar
Bartov, E.; Mohanram, P. S.; and Nissim, D.. “Stock Option Expense, Forward-Looking Information, and Implied Volatilities of Traded Options.” Working Paper, Columbia University and New York University (2004).Google Scholar
Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (1973), 637–654.Google Scholar
Bollerslev, T., and Mikkelsen, H. O.. “Modeling and Pricing Long Memory in Stock Market Volatility.” Journal of Econometrics, 73 (1996), 151–184.Google Scholar
Bollerslev, T., and Mikkelsen, H. O.. “Long-Term Equity Anticipation Securities and Stock Market Volatility Dynamics.” Journal of Econometrics, 92 (1999), 75–99.Google Scholar
Carpenter, J. N. “The Exercise and Valuation of Executive Stock Options.” Journal of Financial Economics, 48 (1998), 127–158.Google Scholar
Carpenter, J. N., and Remmers, B.. “Executive Stock Option Exercises and Inside Information.” Journal of Business, 74 (2001), 513–534.Google Scholar
Christie, A. A. “The Stochastic Behavior of Common Stock Variances: Value, Leverage, and Interest Rate Effects.” Journal of Financial Economics, 10 (1982), 407–432.Google Scholar
Corsi, F. “A Simple Long Memory Model of Realized Volatility.” Working Paper, University of Lugano and Swiss Finance Institute (2004).CrossRefGoogle Scholar
Deo, R. S., and Hurvich, C. M.. “Linear Trend with Fractionally Integrated Errors.” Journal of Time Series Analysis, 19 (1998), 379–397.Google Scholar
Deo, R. S., and Hurvich, C. M.. “On the Log Periodogram Regression Estimator of the Memory Parameter in Long Memory Stochastic Volatility Models.” Econometric Theory, 17 (2001), 686–710.Google Scholar
Deo, R.; Hurvich, C.; and Lu, Y.. “Forecasting Realized Volatility Using a Long-Memory Stochastic Volatility Model: Estimation, Prediction and Seasonal Adjustment.” Journal of Econometrics, 131 (2006), 29–58.Google Scholar
Ding, Z.; Granger, C. W. J.; and Engle, R. F.. “A Long Memory Property of Stock Market Returns and a New Model.” Journal of Empirical Finance, 1 (1993), 83–106.CrossRefGoogle Scholar
French, K. R; Schwert, G. W.; and Stambaugh, R. F.. “Expected Stock Returns and Volatility.” Journal of Financial Economics, 19 (1987), 3–29.Google Scholar
Geweke, J., and Porter-Hudak, S.. “The Estimation and Application of Long Memory Time Series Models.” Journal of Time Series Analysis, 4 (1983), 221–238.Google Scholar
Heath, C.; Huddart, S.; and Lang, M.. “Psychological Factors and Stock Option Exercise.” Quarterly Journal of Economics, 114 (1999), 601–627.Google Scholar
Hemmer, T.; Matsunaga, S.; and Shevlin, S.. “Optimal Exercise and the Cost of Granting Employee Stock Options with a Reload Provision.” Journal of Accounting Research, 36 (1998), 231–255.Google Scholar
Hodder, L. D; Mayew, W. J; McAnally, M. L.; and Weaver, C. D.. “Employee Stock Option Fair-Value Estimates: Do Managerial Discretion and Incentives Explain Accuracy?” Working Paper, Texas A&M University (2006).Google Scholar
Huddart, S., and Lang, M.. “Employee Stock Option Exercises: An Empirical Analysis.” Journal of Accounting and Economics, 21 (1996), 5–43.Google Scholar
Huddart, S., and Lang, M.. “Information Distribution within Firms: Evidence from Stock Option Exercises.” Journal of Accounting and Economics, 34 (2003), 3–31.Google Scholar
Hurvich, C. M., and Deo, R. S.. “Plug-In Selection of the Number of Frequencies in Regression Estimates of the Memory Parameter of a Long-Memory Time Series.” Journal of Time Series Analysis, 20 (1999), 331–341.Google Scholar
Hurvich, C. M.; Deo, R.; and Brodsky, J.. “The Mean Squared Error of Geweke and Porter-Hudak’s Estimator of the Memory Parameter of a Long-Memory Time Series.” Journal of Time Series Analysis, 19 (1998), 19–46.Google Scholar
Johnston, D. “Managing Stock Option Expense: The Manipulation of Option-Pricing Model Assumptions.” Contemporary Accounting Research, 23 (2006), 395–425.CrossRefGoogle Scholar
Karolyi, G. A. “A Bayesian Approach to Modeling Stock Return Volatility for Option Valuation.” Journal of Financial and Quantitative Analysis, 28 (1993), 579–594.Google Scholar
Lev, B. “Some Economic Determinants of Time-Series Properties of Earnings.” Journal of Accounting and Economics, 5 (1983), 31–48.Google Scholar
Merton, R. C. “The Theory of Rational Option Pricing.” Bell Journal of Economics and Management Science, 4 (1973), 141–183.Google Scholar
Merton, R. C. “On Estimating the Expected Return on the Market: An Exploratory Investigation.” Journal of Financial Economics, 8 (1980), 323–361.Google Scholar
Patton, A. J. “Volatility Forecast Comparison Using Imperfect Volatility Proxies.” Working Paper, London School of Economics (2007).Google Scholar
Pong, S.; Shackleton, M. B.; Taylor, S. J.; and Xu, X.. “Forecasting Currency Volatility: A Comparison of Implied Volatilities and AR(FI)MA Models.” Journal of Banking and Finance, 28 (2004), 2541–2563.Google Scholar
Poon, S.-H., and Granger, C. W. J.. “Forecasting Volatility in Financial Markets: A Review.” Journal of Economic Literature, 41 (2003), 478–539.Google Scholar
Poterba, J. M., and Summers, L. H.. “The Persistence of Volatility and Stock Market Fluctuations.” American Economic Review, 76 (1986), 1142–1151.Google Scholar
Robinson, P. M. “Gaussian Semiparametric Estimation of Long Range Dependence.” Annals of Statistics, 23 (1995a), 1630–1661.Google Scholar
Robinson, P. M. “Log-Periodogram Regression of Time Series with Long Range Dependence.” Annals of Statistics, 23 (1995b), 1048–1072.Google Scholar
Schwert, G. W. “Why Does Stock Market Volatility Change Over Time?” Journal of Finance, 44 (1989), 1115–1153.Google Scholar
Taqqu, M. S., and Teverovsky, V.. “Robustness of Whittle-Type Estimators for Time Series with Long-Range Dependence.” Stochastic Models, 13 (1997), 723–757.CrossRefGoogle Scholar
Timmermann, A. “Forecast Combinations.” In Handbook of Economic Forecasting, Vol. 1, Elliott, G., Granger, C. W. J., and Timmermann, A., eds. Amsterdam: North-Holland (2006), 135–196.Google Scholar
West, K. “Forecast Evaluation.”In Handbook of Economic Forecasting, Vol. 1, Elliott, G., Granger, C. W. J., and Timmermann, A., eds. Amsterdam: North-Holland (2006), 99–134.Google Scholar