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GARCH Gamma

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  • Robert F. Engle
  • Joshua V. Rosenberg

Abstract

This paper addresses the issue of hedging option positions when the underlying asset exhibits stochastic volatility. By parameterizing the volatility process as GARCH, and utilizing risk- neutral valuation, we estimate hedging parameters (delta and gamma) using Monte-Carlo simulation. We estimate hedging parameters for options on the Standard and Poor's 500 index, a bond futures index, a weighted foreign exchange rate index, and an oil futures index. We find that Black-Scholes and GARCH deltas are similar for all the options considered, while GARCH gammas are significantly higher than BS gammas for all options. For near the money options, GARCH gamma hedge ratios are higher than BS hedge ratios when hedging a long term option with a short term option. Away from the money, GARCH gamma hedge ratios are lower than BS.

Suggested Citation

  • Robert F. Engle & Joshua V. Rosenberg, 1995. "GARCH Gamma," NBER Working Papers 5128, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:5128
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    References listed on IDEAS

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    Cited by:

    1. Robert F. Engle & Joshua Rosenberg, 1966. "Testing the Volatility Term Structure Using Option Hedging Criteria," New York University, Leonard N. Stern School Finance Department Working Paper Seires 96-24, New York University, Leonard N. Stern School of Business-.
    2. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    3. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June.
    4. Malik, Farooq & Ewing, Bradley T., 2009. "Volatility transmission between oil prices and equity sector returns," International Review of Financial Analysis, Elsevier, vol. 18(3), pages 95-100, June.
    5. Peter Hans Matthews, 2005. "Paradise lost and found? The econometric contributions of Clive W. J. Granger and Robert F. Engle," Review of Political Economy, Taylor & Francis Journals, vol. 17(1), pages 1-28.
    6. Francis X. Diebold, 2004. "The Nobel Memorial Prize for Robert F. Engle," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(2), pages 165-185, June.
    7. Badescu, Alexandru & Elliott, Robert J. & Ortega, Juan-Pablo, 2014. "Quadratic hedging schemes for non-Gaussian GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 13-32.
    8. Walsh, David M., 1999. "Some exotic options under symmetric and asymmetric conditional volatility of returns," Journal of Multinational Financial Management, Elsevier, vol. 9(3-4), pages 403-417, November.
    9. Hall, Stephen & Mizon, Grayham E. & Welfe, Aleksander, 2000. "Modelling economies in transition: an introduction," Economic Modelling, Elsevier, vol. 17(3), pages 339-357, August.

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