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A Test of Efficiency for the S&P Index Option Market Using Variance Forecasts

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  • Jaesun Noh
  • Robert F. Engle
  • Alex Kane

Abstract

To forecast future option prices, autoregressive models of implied volatility derived from observed option prices are commonly employed [see Day and Lewis (1990), and Harvey and Whaley (1992)]. In contrast, the ARCH model proposed by Engle (1982) models the dynamic behavior in volatility, forecasting future volatility using only the return series of an asset. We assess the performance of these two volatility prediction models from S&P 500 index options market data over the period from September 1986 to December 1991 by employing two agents who trade straddles, each using one of the two different methods of forecast. Straddle trading is employed since a straddle does not need to be hedged. Each agent prices options according to her chosen method of forecast, buying (selling) straddles when her forecast price for tomorrow is higher (lower) than today's market closing price, and at the end of each day the rates of return are computed. We find that the agent using the GARCH forecast method earns greater profit than the agent who uses the implied volatility regression (IVR) forecast model. In particular, the agent using the GARCH forecast method earns a profit in excess of a cost of $0.25 per straddle with the near-the-money straddle trading.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 4520.

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Date of creation: Nov 1993
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Publication status: published as (Published as "Forecasting Volatility and Option Prices of the S & P 500 Index") Journal of Derivatives, Vol. 2 (1994): 17-30.
Handle: RePEc:nbr:nberwo:4520

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  1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  2. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 19(1), pages 3-29, September.
  3. Pindyck, Robert S., 1983. "Risk, inflation, and the stock market," Working papers, Massachusetts Institute of Technology (MIT), Sloan School of Management 1423-83., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
  5. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 9(4), pages 345-59, October.
  6. Pagan, Adrian R. & Schwert, G. William, 1990. "Alternative models for conditional stock volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 45(1-2), pages 267-290.
  7. Hentschel, Ludger & Campbell, John, 1992. "No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns," Scholarly Articles 3220232, Harvard University Department of Economics.
  8. French, Kenneth R. & Roll, Richard, 1986. "Stock return variances : The arrival of information and the reaction of traders," Journal of Financial Economics, Elsevier, Elsevier, vol. 17(1), pages 5-26, September.
  9. Schwert, G William, 1990. "Stock Volatility and the Crash of '87," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 3(1), pages 77-102.
  10. Tim Bollerslev & Jeffrey M. Wooldridge, 1988. "Quasi-Maximum Likelihood Estimation of Dynamic Models with Time-Varying Covariances," Working papers, Massachusetts Institute of Technology (MIT), Department of Economics 505, Massachusetts Institute of Technology (MIT), Department of Economics.
  11. 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.
  12. 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, Econometric Society, vol. 55(2), pages 391-407, March.
  13. Coulson, N. Edward & Robins, Russell P., 1985. "Aggregate economic activity and the variance of inflation : Another look," Economics Letters, Elsevier, Elsevier, vol. 17(1-2), pages 71-75.
  14. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 347-70, March.
  15. Chou, Ray Yeutien, 1988. "Volatility Persistence and Stock Valuations: Some Empirical Evidence Using Garch," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 3(4), pages 279-94, October-D.
  16. Whaley, Robert E., 1982. "Valuation of American call options on dividend-paying stocks : Empirical tests," Journal of Financial Economics, Elsevier, Elsevier, vol. 10(1), pages 29-58, March.
  17. Domowitz, Ian & Hakkio, Craig S., 1985. "Conditional variance and the risk premium in the foreign exchange market," Journal of International Economics, Elsevier, Elsevier, vol. 19(1-2), pages 47-66, August.
  18. Day, Theodore E. & Lewis, Craig M., 1988. "The behavior of the volatility implicit in the prices of stock index options," Journal of Financial Economics, Elsevier, Elsevier, vol. 22(1), pages 103-122, October.
  19. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 281-300, June.
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Cited by:
  1. Rafiqul Bhuyan, 2002. "Information, Alternative Markets, and Security Price Processes: A Survey of Literature," Finance, EconWPA 0211002, EconWPA.
  2. Brock Johnson & Jonathan Batten, 2003. "Forecasting Credit Spread Volatility: Evidence from the Japanese Eurobond Market," Asia-Pacific Financial Markets, Springer, Springer, vol. 10(4), pages 335-357, December.

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