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Testing the Volatility Term Structure Using Option Hedging Criteria

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  • Robert F. Engle
  • Joshua Rosenberg

Abstract

The volatility term structure (VTS) reflects market expectations of asset volatility over different horizons. These expectations change over time, giving dynamic structure to the VTS. This paper evaluates volatility models on the basis of their performance in hedging option price changes due to shifts in the VTS. An innovative feature of the hedging approach is its increased sensitivity to several important forms of model misspecification relative to previous testing methods. Volatility hedge parameters are derived for several volatility models incorporating different predicted VTS dynamics and information variables. Hedging tests using S&P500 index options indicate that the GARCH components with leverage VTS estimate is most accurate. Evidence is obtained for mean-reversion in volatility and correlation between VTS shifts and S&P500 returns. While a convexity hedge dominates the volatility hedges for the observed sample, this result appears to be due to sample selection bias.

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Bibliographic Info

Paper provided by New York University, Leonard N. Stern School of Business- in its series New York University, Leonard N. Stern School Finance Department Working Paper Seires with number 96-24.

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Date of creation: Apr 1966
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Handle: RePEc:fth:nystfi:96-24

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Postal: U.S.A.; New York University, Leonard N. Stern School of Business, Department of Economics . 44 West 4th Street. New York, New York 10012-1126
Phone: (212) 998-0100
Web page: http://w4.stern.nyu.edu/finance/
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  1. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  2. Hull, John & White, Alan, 1987. "Hedging the risks from writing foreign currency options," Journal of International Money and Finance, Elsevier, vol. 6(2), pages 131-152, June.
  3. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  4. Robert F. Engle & Joshua V. Rosenberg, 1995. "GARCH Gamma," NBER Working Papers 5128, National Bureau of Economic Research, Inc.
  5. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
  6. Amin, Kaushik I & Ng, Victor K, 1993. " Option Valuation with Systematic Stochastic Volatility," Journal of Finance, American Finance Association, vol. 48(3), pages 881-910, July.
  7. Heynen, Ronald & Kemna, Angelien & Vorst, Ton, 1994. "Analysis of the Term Structure of Implied Volatilities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(01), pages 31-56, March.
  8. 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.
  9. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204.
  10. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
  11. Stein, Jeremy, 1989. " Overreactions in the Options Market," Journal of Finance, American Finance Association, vol. 44(4), pages 1011-23, September.
  12. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
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  14. Melino, Angelo & Turnbull, Stuart M., 1995. "Misspecification and the pricing and hedging of long-term foreign currency options," Journal of International Money and Finance, Elsevier, vol. 14(3), pages 373-393, June.
  15. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
  16. 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.
  17. Xu, Xinzhong & Taylor, Stephen J., 1994. "The Term Structure of Volatility Implied by Foreign Exchange Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(01), pages 57-74, March.
  18. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
  19. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
  20. 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. Christopher J. Neely, 2004. "Implied volatility from options on gold futures: do statistical forecasts add value or simply paint the lilly?," Working Papers 2003-018, Federal Reserve Bank of St. Louis.
  2. Christopher J. Neely, 2004. "Forecasting foreign exchange volatility: why is implied volatility biased and inefficient? and does it matter?," Working Papers 2002-017, Federal Reserve Bank of St. Louis.
  3. Pilar Corredor-Casado & Rafael Santamaría-Aquilué, 2000. "La estructura temporal de las volatilidades implícitas en la opción sobre el IBEX-35," Investigaciones Economicas, Fundación SEPI, vol. 24(2), pages 385-417, May.
  4. Francis X. Diebold, 2004. "The Nobel Memorial Prize for Robert F. Engle," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(2), pages 165-185, 06.
  5. Bronka Rzepkowski, 2003. "Order Flows, Delta Hedging and Exchange Rate Dynamics," Working Papers 2003-18, CEPII research center.
  6. Agnolucci, Paolo, 2009. "Volatility in crude oil futures: A comparison of the predictive ability of GARCH and implied volatility models," Energy Economics, Elsevier, vol. 31(2), pages 316-321, March.
  7. Tobias Adrian & Erkko Etula, 2010. "Funding liquidity risk and the cross-section of stock returns," Staff Reports 464, Federal Reserve Bank of New York.
  8. Tobias Adrian & Joshua Rosenberg, 2006. "Stock returns and volatility: pricing the short-run and long-run components of market risk," Staff Reports 254, Federal Reserve Bank of New York.
  9. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
  10. Christopher J. Neely & Drew B. Winters, 2005. "Year-end seasonality in one-month LIBOR derivatives," Working Papers 2003-040, Federal Reserve Bank of St. Louis.

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