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The Economic Value of Realized Volatility: Using High-Frequency Returns for Option Valuation

  • Peter Christoffersen (a1), Bruno Feunou (a2), Kris Jacobs (a3) and Nour Meddahi (a4)
Abstract

Many studies have documented that daily realized volatility estimates based on intraday returns provide volatility forecasts that are superior to forecasts constructed from daily returns only. We investigate whether these forecasting improvements translate into economic value added. To do so, we develop a new class of affine discrete-time option valuation models that use daily returns as well as realized volatility. We derive convenient closed-form option valuation formulas, and we assess the option valuation properties using Standard & Poor’s (S&P) 500 return and option data. We find that realized volatility reduces the pricing errors of the benchmark model significantly across moneyness, maturity, and volatility levels.

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Aït-Sahalia, Y., and Jacod, J.. “Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data.” Journal of Economic Literature, 50 (2012), 10071050.
Aït-Sahalia, Y., and Kimmel, R.. “Maximum Likelihood Estimation of Stochastic Volatility Models.” Journal of Financial Economics, 83 (2007), 413452.
Andersen, T. G., and Bollerslev, T.. “Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts.” International Economic Review, 39 (1998), 885905.
Andersen, T. G.; Bollerslev, T.; Diebold, F. X.; and Labys, P.. “Modeling and Forecasting Realized Volatility.” Econometrica, 71 (2003), 579625.
Andersen, T. G.; Fusari, N.; and Todorov, V.. “Parametric Inference and Dynamic State Recovery from Option Panels.” Working Paper, Northwestern University(2012).
Andrews, D. “Tests for Parameter Instability and Structural Change with Unknown Change Point.” Econometrica, 61 (1993), 821856.
Andrews, D. “Testing When a Parameter Is on the Boundary of the Maintained Hypothesis.”Econometrica, 69 (2001), 683734.
Andrews, D., and Ploberger, W.. “Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative.” Econometrica, 62 (1994), 13831414.
Barndorff-Nielsen, O. E., and Shephard, N.. “Econometric Analysis of Realized Volatility and Its Use in Estimating Stochastic Volatility Models.” Journal of the Royal Statistical Society, B, 64 (2002), 253280.
Barone-Adesi, G.; Engle, R.; and Mancini, L.. “A GARCH Option Pricing Model with Filtered Historical Simulation.” Review of Financial Studies, 21 (2008), 12231258.
Bates, D. “Testing Option Pricing Models.” In Handbook of Statistics, Statistical Methods in Finance, Maddala, G. S. and Rao, C. R., eds. Amsterdam: Elsevier (1996), pp. 567611.
Bates, D. “Post-87 Crash Fears in S&P 500 Futures Options.” Journal of Econometrics, 94 (2000), 181238.
Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (1973), 637654.
Bollerslev, T. “Generalized Autoregressive Conditional Heteroskedasticity.” Journal of Econometrics, 31 (1986), 307327.
Bollerslev, T.; Kretschmer, U.; Pigorsch, C.; and Tauchen, G.. “A Discrete-Time Model for Daily S&P 500 Returns and Realized Variations: Jumps and Leverage Effects.” Journal of Econometrics, 150 (2009), 151166.
Bollerslev, T., and Mikkelsen, H.. “Long-Term Equity Anticipation Securities and Stock Market Volatility Dynamics.” Journal of Econometrics, 92 (1999), 7599.
Bollerslev, T., and Wooldridge, J. M.. “Quasi-Maximum Likelihood Estimation and Inference in Dynamic Models with Time-Varying Covariances.” Econometric Reviews, 11 (1992), 143172.
Chen, X.; Ghysels, E.; and Wang, F.. “HYBRID GARCH Models and Intra-Daily Return Periodicity.” Journal of Time Series Econometrics, 3 (2011), 1941–1928.
Chernov, M.; Gallant, A. R.; Ghysels, E.; and Tauchen, G.. “Alternative Models for Stock Price Dynamics.” Journal of Econometrics, 116 (2003), 225257.
Cho, S. J., and White, H.. “Testing for Regime Switching.” Econometrica, 75 (2007), 16711720.
Christoffersen, P.; Dorion, C.; Jacobs, K.; and Wang, Y.. “Volatility Components, Affine Restrictions, and Nonnormal Innovations.” Journal of Business and Economic Statistics, 28 (2010), 483502.
Christoffersen, P.; Elkamhi, R.; Feunou, B.; and Jacobs, K.. “Option Valuation with Conditional Heteroskedasticity and Nonnormality.” Review of Financial Studies, 23 (2010), 21392183.
Christoffersen, P.; Heston, S.; and Jacobs, K.. “The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well.” Management Science, 55 (2009), 19141932.
Christoffersen, P.; Jacobs, K.; and Mimouni, K.. “Volatility Dynamics for the S&P500: Evidence from Realized Volatility, Daily Returns, and Option Prices.” Review of Financial Studies, 23 (2010), 31413189.
Christoffersen, P.; Jacobs, K.; Ornthanalai, C.; and Wang, Y.. “Option Valuation with Long-Run and Short-Run Volatility Components.” Journal of Financial Economics, 90 (2008), 272297.
Corsi, F.; Fusari, N.; and La Vecchia, D.. “Realizing Smiles: Options Pricing with Realized Volatility.” Journal of Financial Economics, 107 (2013), 284304.
Duan, J. C. “The GARCH Option Pricing Model.” Mathematical Finance, 5 (1995), 1332.
Engle, R. “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of UK Inflation.” Econometrica, 50 (1982), 9871008.
Engle, R. “New Frontiers in ARCH Models.” Journal of Applied Econometrics, 17 (2002), 425446.
Engle, R., and Gallo, G.. “A Multiple Indicators Model for Volatility Using Intra-Daily Data.” Journal of Econometrics, 131 (2006), 327.
Engle, R., and Mustafa, C.. “Implied ARCH Models from Options Prices.” Journal of Econometrics, 52 (1992), 289311.
Engle, R., and Ng, V.. “Measuring and Testing the Impact of News on Volatility.” Journal of Finance, 48 (1993), 17491778.
Forsberg, L., and Bollerslev, T.. “Bridging the Gap Between the Distribution of Realized (ECU) and ARCH Modelling (of the Euro): The GARCH-NIG Model.” Journal of Applied Econometrics, 17 (2002), 535548.
French, K.; Schwert, G. W.; and Stambaugh, R.. “Expected Stock Returns and Volatility.” Journal of Financial Economics, 19 (1987), 330.
Glosten, L.; Jagannathan, R.; and Runkle, D.. “On the Relation Between the Expected Value and the Volatility of the Nominal Excess Return on Stocks.” Journal of Finance, 48 (1993), 17791801.
Gourieroux, C.; Monfort, A.; and Trognon, A.. “Pseudo Maximum Likelihood Methods: Theory.” Econometrica, 52 (1984), 681700.
Hansen, P.; Huang, Z.; and Shek, H.. “Realized GARCH: A Joint Model for Returns and Realized Measures of Volatility.” Journal of Applied Econometrics, 27 (2012), 877906.
Hansen, P., and Lunde, A.. “A Realized Variance for the Whole Day Based on Intermittent High-Frequency Data.” Journal of Financial Econometrics, 3 (2005), 525554.
Heston, S., and Nandi, S.. “A Closed-Form GARCH Option Pricing Model.” Review of Financial Studies, 13 (2000), 585626.
Hsieh, K., and Ritchken, P.. “An Empirical Comparison of GARCH Option Pricing Models.” Review of Derivatives Research, 8 (2005), 129150.
Jones, C. “The Dynamics of Stochastic Volatility: Evidence from Underlying and Options Markets.” Journal of Econometrics, 116 (2003), 181224.
Mincer, J., and Zarnowitz, V.. “The Evaluation of Economic Forecasts.” In Economic Forecasts and Expectations, Mincer, J., ed. New York: National Bureau of Economic Research (1969).
Nelson, D. B. “Conditional Heteroskedasticity in Asset Returns: A New Approach.” Econometrica, 59 (1991), 347370.
Renault, E. “Econometric Models of Option Pricing Errors.” In Advances in Economics and Econometrics, Seventh World Congress, Kreps, D. M. and Wallis, K. F., eds. New York, NY: Econometric Society Monographs, Cambridge University Press (1997), pp. 223278.
Ritchken, P., and Trevor, R.. “Pricing Options Under Generalized GARCH and Stochastic Volatility Processes.” Journal of Finance, 54 (1999), 377402.
Shephard, N., and Sheppard, K.. “Realising the Future: Forecasting with High-Frequency-Based Volatility (Heavy) Models.” Journal of Applied Econometrics, 25 (2010), 197231.
Stentoft, L. “Option Pricing Using Realized Volatility.” Working Paper, University of Aarhus(2008).
Trolle, A., and Schwartz, E.. “Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives.” Review of Financial Studies, 22 (2009), 44234461.
Zhang, L.; Mykland, P.; and Aït-Sahalia, Y.. “A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High-Frequency Data.” Journal of the American Statistical Association, 100 (2005), 13941411.
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  • ISSN: 0022-1090
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