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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.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 5128.

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Date of creation: May 1995
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Publication status: published as Robert F . Engle Joshua V . Rosenberg. "GARCH Gamma" Journal of Derivatives, Summer 1995, Vol. 2, No. 4: pp. 47-59
Handle: RePEc:nbr:nberwo:5128

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  1. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, Elsevier, vol. 4(3), pages 323-338, May.
  2. Gilster, John E., 1990. "The Systematic Risk of Discretely Rebalanced Option Hedges," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 25(04), pages 507-516, December.
  3. Chen, Nai-fu & Johnson, Herb, 1985. "Hedging options," Journal of Financial Economics, Elsevier, Elsevier, vol. 14(2), pages 317-321, June.
  4. Johnson, Herb & Shanno, David, 1987. "Option Pricing when the Variance Is Changing," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 22(02), pages 143-151, June.
  5. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 22(04), pages 419-438, December.
  6. Boyle, Phelim P. & Emanuel, David, 1980. "Discretely adjusted option hedges," Journal of Financial Economics, Elsevier, Elsevier, vol. 8(3), pages 259-282, September.
  7. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(1-2), pages 145-166.
  8. Brennan, M J, 1979. "The Pricing of Contingent Claims in Discrete Time Models," Journal of Finance, American Finance Association, American Finance Association, vol. 34(1), pages 53-68, March.
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  24. Hull, John & White, Alan, 1987. "Hedging the risks from writing foreign currency options," Journal of International Money and Finance, Elsevier, Elsevier, vol. 6(2), pages 131-152, June.
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Citations

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Cited by:
  1. Joshua Rosenberg & Robert F. Engle, 2000. "Empirical Pricing Kernels," New York University, Leonard N. Stern School Finance Department Working Paper Seires, New York University, Leonard N. Stern School of Business- 99-014, New York University, Leonard N. Stern School of Business-.
  2. 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, Taylor & Francis Journals, vol. 17(1), pages 1-28.
  3. Hall, S. & Mizon, G.E. & Welfe, A., 1999. "Modelling economies in transition: an introduction," Discussion Paper Series In Economics And Econometrics 9919, Economics Division, School of Social Sciences, University of Southampton.
  4. Francis X. Diebold, 2004. "The Nobel Memorial Prize for Robert F. Engle," Scandinavian Journal of Economics, Wiley Blackwell, Wiley Blackwell, vol. 106(2), pages 165-185, 06.
  5. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, School of Economics and Management, University of Aarhus.
  6. Walsh, David M., 1999. "Some exotic options under symmetric and asymmetric conditional volatility of returns," Journal of Multinational Financial Management, Elsevier, Elsevier, vol. 9(3-4), pages 403-417, November.
  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, Elsevier, vol. 42(C), pages 13-32.
  8. Malik, Farooq & Ewing, Bradley T., 2009. "Volatility transmission between oil prices and equity sector returns," International Review of Financial Analysis, Elsevier, Elsevier, vol. 18(3), pages 95-100, June.
  9. Robert F. Engle & Joshua Rosenberg, 1998. "Testing the Volatility Term Structure using Option Hedging Criteria," New York University, Leonard N. Stern School Finance Department Working Paper Seires, New York University, Leonard N. Stern School of Business- 98-031, New York University, Leonard N. Stern School of Business-.

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