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Index-Option Pricing with Stochastic Volatility and the Value of Accurate Variance Forecasts

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  • Robert F. Engle
  • Alex Kane
  • Jaesun Noh

Abstract

In pricing primary-market options and in making secondary markets, financial intermediaries depend on the quality of forecasts of the variance of the underlying assets. Hence, the gain from improved pricing of options would be a measure of the value of a forecast of underlying asset returns. NYSE index returns over the period of 1968-1991 are used to suggest that pricing index options of up to 90-days maturity would be more accurate when: (1) using ARCH specifications in place of a moving average of squared returns; (2) using Hull and White's (1987) adjustment for stochastic variance in Black and Scholes's (1973) formula; (3) accounting explicitly for weekends and the slowdown of variance whenever the market is closed.

Suggested Citation

  • Robert F. Engle & Alex Kane & Jaesun Noh, 1993. "Index-Option Pricing with Stochastic Volatility and the Value of Accurate Variance Forecasts," NBER Working Papers 4519, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:4519 Note: AP
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    References listed on IDEAS

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    1. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    2. Richardson, Matthew & Stock, James H., 1989. "Drawing inferences from statistics based on multiyear asset returns," Journal of Financial Economics, Elsevier, vol. 25(2), pages 323-348, December.
    3. French, Kenneth R. & Roll, Richard, 1986. "Stock return variances : The arrival of information and the reaction of traders," Journal of Financial Economics, Elsevier, vol. 17(1), pages 5-26, September.
    4. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    5. Brenner, Menachem & Galai, Dan, 1986. "Implied Interest Rates," The Journal of Business, University of Chicago Press, vol. 59(3), pages 493-507, July.
    6. 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 637-654, May-June.
    7. Matthew Richardson & James H. Stock, 1990. "Drawing Inferences From Statistics Based on Multi-Year Asset Returns," NBER Working Papers 3335, National Bureau of Economic Research, Inc.
    8. 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.
    9. 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.
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    Citations

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    Cited by:

    1. Eric Jacquier & Robert Jarrow, "undated". "Model Error in Contingent Claim Models (Dynamic Evaluation)," Rodney L. White Center for Financial Research Working Papers 7-96, Wharton School Rodney L. White Center for Financial Research.
    2. Xekalaki, Evdokia & Degiannakis, Stavros, 2005. "Evaluating volatility forecasts in option pricing in the context of a simulated options market," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 611-629, April.
    3. Ayla Ogus, 2002. "Pricing of S&P 100 Index Options Based On Garch Volatility Estimates," Working Papers 0201, Izmir University of Economics.
    4. Lopez, Jose A, 2001. "Evaluating the Predictive Accuracy of Volatility Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(2), pages 87-109, March.
    5. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
    6. LUBRANO, Michel, 1998. "Smooth transition GARCH models: a Bayesian perspective," CORE Discussion Papers 1998066, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Michael S. Gibson & Brian H. Boyer, 1997. "Evaluating forecasts of correlation using option pricing," International Finance Discussion Papers 600, Board of Governors of the Federal Reserve System (U.S.).
    8. Gonzalez-Rivera, Gloria & Lee, Tae-Hwy & Mishra, Santosh, 2004. "Forecasting volatility: A reality check based on option pricing, utility function, value-at-risk, and predictive likelihood," International Journal of Forecasting, Elsevier, vol. 20(4), pages 629-645.
    9. Miguel A. Ferreira, 2005. "Evaluating Interest Rate Covariance Models Within a Value-at-Risk Framework," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(1), pages 126-168.
    10. Catalin Starica & Stefano Herzel & Tomas Nord, 2005. "Why does the GARCH(1,1) model fail to provide sensible longer- horizon volatility forecasts?," Econometrics 0508003, EconWPA.
    11. Schmitt, Christian & Kaehler, Jürgen, 1996. "Delta-neutral volatility trading with intra-day prices: an application to options on the DAX," ZEW Discussion Papers 96-25, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    12. Holger Claessen & Stefan Mittnik, 2002. "Forecasting stock market volatility and the informational efficiency of the DAX-index options market," The European Journal of Finance, Taylor & Francis Journals, vol. 8(3), pages 302-321.
    13. Gregory Connor & Lisa R. Goldberg & Robert A. Korajczyk, 2010. "Portfolio Risk Analysis," Economics Books, Princeton University Press, edition 1, number 9224, June.
    14. Jose A. Lopez & Christian Walter, 2000. "Evaluating covariance matrix forecasts in a value-at-risk framework," Working Paper Series 2000-21, Federal Reserve Bank of San Francisco.
    15. David Bates & Roger Craine, 1998. "Valuing the Futures Market Clearinghouse's Default Exposure During the 1987 Crash," NBER Working Papers 6505, National Bureau of Economic Research, Inc.
    16. Stavros Degiannakis & Alexandra Livada & Epaminondas Panas, 2008. "Rolling-sampled parameters of ARCH and Levy-stable models," Applied Economics, Taylor & Francis Journals, vol. 40(23), pages 3051-3067.
    17. Jaesun Noh & Robert F. Engle & Alex Kane, 1993. "A Test of Efficiency for the S&P Index Option Market Using Variance Forecasts," NBER Working Papers 4520, National Bureau of Economic Research, Inc.
    18. Angelidis, Timotheos & Degiannakis, Stavros, 2008. "Volatility forecasting: intra-day vs. inter-day models," MPRA Paper 80434, University Library of Munich, Germany.
    19. James Chong, 2004. "Options trading profits from correlation forecasts," Applied Financial Economics, Taylor & Francis Journals, vol. 14(15), pages 1075-1085.
    20. Dajiang Guo, 2000. "Dynamic Volatility Trading Strategies in the Currency Option Market," Review of Derivatives Research, Springer, vol. 4(2), pages 133-154, May.

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