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Hedging Options in a GARCH Environment: Testing the Term Structure of Stochastic Volatility Models

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  • Robert F. Engle
  • Joshua Rosenberg

Abstract

This paper develops a methodology for testing the term structure of volatility forecasts derived from stochastic volatility models, and implements it to analyze models of S&P 500 index volatility. Volatility models are compared by their ability to hedge options positions sensitive to the term structure of volatility. Overall, the most effective hedge is a Black-Scholes (BS) delta-gamma hedge, while the BS delta-vega hedge is the least effective. The most successful volatility hedge is GARCH components delta-gamma, suggesting that the GARCH components estimate of the term structure of volatility is most accurate. The success of the BS delta-gamma hedge may be due to mispricing in the options market over the sample period.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 4958.

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Date of creation: Dec 1994
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Publication status: Published as "Bayesian Analysis of Stochastic Volatility Models: Comment", JBES, Vol. 12, no. 4 (1994): 395-396.
Handle: RePEc:nbr:nberwo:4958

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  1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  2. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  3. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
  4. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
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Cited by:
  1. Jacobi, Frank, 2005. "ARCH-Prozesse und ihre Erweiterungen - Eine empirische Untersuchung für Finanzmarktzeitreihen -," Arbeitspapiere des Instituts für Statistik und Ökonometrie 31, Johannes Gutenberg-Universität Mainz, Institut für Statistik und Ökonometrie.
  2. Guillermo Benavides & Carlos Capistrán, 2009. "Forecasting Exchange Rate Volatility: The Superior Performance of Conditional Combinations of Time Series and Option Implied Forecasts," Working Papers 2009-01, Banco de México.
  3. Deschamps, Philippe J., 2011. "Bayesian Estimation of Generalized Hyperbolic Skewed Student GARCH Models," DQE Working Papers 16, Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland, revised 09 Jun 2012.
  4. Goeij, P. C. de & Marquering, W., 2004. "Modeling the conditional covariance between stock and bond returns: A multivariate GARCH approach," Open Access publications from Tilburg University urn:nbn:nl:ui:12-194709, Tilburg University.
  5. Robert F. Engle & Joshua V. Rosenberg, 1995. "GARCH Gamma," NBER Working Papers 5128, National Bureau of Economic Research, Inc.
  6. Matei, Marius, 2011. "Non-Linear Volatility Modeling of Economic and Financial Time Series Using High Frequency Data," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 116-141, June.
  7. Christensen, Kim & Podolski, Mark, 2005. "Asymptotic theory for range-based estimation of integrated variance of a continuous semi-martingale," Technical Reports 2005,18, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  8. Shirley J. Huang & Qianqiu Liu & Jun Yu, 2007. "Realized Daily Variance of S&P 500 Cash Index: A Revaluation of Stylized Facts," Annals of Economics and Finance, Society for AEF, vol. 8(1), pages 33-56, May.

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