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Evaluating forecasts of correlation using option pricing

  • Michael S. Gibson
  • Brian H. Boyer
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    A forecast of the correlation between two asset prices is required to price or hedge an option whose payoff depends on both asset prices or to measure the risk of a portfolio whose return depends on both asset prices. However, a number of factors make it difficult to evaluate forecasts of correlation. We develop a forecast evaluation methodology based on option pricing, extending a technique that Engle et al. (1993) introduced to evaluate volatility forecasts. A forecast of the variance-covariance matrix of joint asset returns is used to generate a trading strategy for a package of simulated options. The most accurate forecast will produce the most profitable trading strategy. The package of simulated options can be chosen to be sensitive to correlation, to volatility, or to any arbitrary combination of the two. In an empirical application, we focus on the ability to forecast the correlation between two stock market indices. We compare the correlation forecasting ability of three more sophisticated models (two GARCH models and a two-state Markov switching model) and two simple moving averages. We find that the more sophisticated models produce better correlation forecasts than the simple moving averages.

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    File URL: http://www.federalreserve.gov/pubs/ifdp/1997/600/default.htm
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    File URL: http://www.federalreserve.gov/pubs/ifdp/1997/600/ifdp600.pdf
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    Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series International Finance Discussion Papers with number 600.

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    Date of creation: 1997
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    Handle: RePEc:fip:fedgif:600
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    1. Jose M. Campa & P. H. Kevin Chang, 1997. "The Forecasting Ability of Correlations Implied in Foreign Exchange Options," NBER Working Papers 5974, National Bureau of Economic Research, Inc.
    2. Robert F. Engle & Che-Hsiung Hong & Alex Kane, 1990. "Valuation of Variance Forecast with Simulated Option Markets," NBER Working Papers 3350, National Bureau of Economic Research, Inc.
    3. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-66, July.
    4. 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.
    5. Kenneth D. West & Dongchul Cho, 1994. "The Predictive Ability of Several Models of Exchange Rate Volatility," NBER Technical Working Papers 0152, National Bureau of Economic Research, Inc.
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    7. Stulz, ReneM., 1982. "Options on the minimum or the maximum of two risky assets : Analysis and applications," Journal of Financial Economics, Elsevier, vol. 10(2), pages 161-185, July.
    8. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
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    10. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
    11. 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.
    12. Christian Walter & Jose Lopez, 1997. "Is implied correlation worth calculating? Evidence from foreign exchange options and historical data," Research Paper 9730, Federal Reserve Bank of New York.
    13. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-86, March.
    14. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
    15. Baillie, R.T. & Bollerslev, R.T., 1990. "Prediction In Dynamic Models With Time Dependent Conditional Variances," Papers 8815, Michigan State - Econometrics and Economic Theory.
    16. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-44, January.
    17. 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, vol. 96(1), pages 116-31, February.
    18. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    19. Jorion, Philippe, 1995. " Predicting Volatility in the Foreign Exchange Market," Journal of Finance, American Finance Association, vol. 50(2), pages 507-28, June.
    20. 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.
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