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Valuation of Variance Forecast with Simulated Option Markets

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  • Robert F. Engle
  • Che-Hsiung Hong
  • Alex Kane

Abstract

An appropriate metric for the success of an algorithm to forecast the variance of the rate of return on a capital asset could be the incremental profit from substituting it for the next best alternative. We propose a framework to assess incremental profits for competing algorithms to forecast the variance of a prespecified asset. The test is based on the return history of the asset in question. A hypothetical insurance market is set up, where competing forecasting algorithms are used. One algorithm is used by each hypothetical agent in an "ex post ante" forecasting exercise, using the available history of the asset returns. The profit differentials across agents (in various groupings) reflect incremental values of the forecasting algorithms. The technique is demonstrated with the NYSE portfolio, over the period of July 22, 1966 to December 31, 1985. For the limited set of alternative specifications, we find that GARCH(1,1) yields better profits than the 3 competing specifications. The profit from pricing one-day options on the NYSE portfolio significant. The evidence also suggests that using a limited estimation period may be preferable to estimating specification parameters from all available observations. Finally, the hedging activity that requires a variance determined hedge ratio is an important component of the success of a variance forecast-algorithm.

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File URL: http://www.nber.org/papers/w3350.pdf
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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 3350.

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Date of creation: May 1990
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Publication status: published as Robert Engle, Che-Hsuing Hong, Alex Kane, and Jaesun Noh, "Arbitrage Valuation of Variance Forecasts with Simulated Options," Advances in Futures and Options Research, Vol. 6, 1992, pp. 393-416.
Handle: RePEc:nbr:nberwo:3350

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  1. Adrian R. Pagan & G. William Schwert, 1990. "Alternative Models For Conditional Stock Volatility," NBER Working Papers 2955, National Bureau of Economic Research, Inc.
  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. 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.
  4. Merton, Robert C, 1981. "On Market Timing and Investment Performance. I. An Equilibrium Theory of Value for Market Forecasts," The Journal of Business, University of Chicago Press, vol. 54(3), pages 363-406, July.
  5. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 96(1), pages 116-31, February.
  6. Schmalensee, Richard & Trippi, Robert R, 1978. "Common Stock Volatility Expectations Implied by Option Premia," Journal of Finance, American Finance Association, American Finance Association, vol. 33(1), pages 129-47, March.
  7. Pagan, Adrian & Ullah, Aman, 1988. "The Econometric Analysis of Models with Risk Terms," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 3(2), pages 87-105, April.
  8. Zvi Bodie, 1988. "Inflation, Index-Linked Bonds, and Asset Allocation," NBER Working Papers 2793, National Bureau of Economic Research, Inc.
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