GARCH Gamma

26 Pages Posted: 15 Jul 2000 Last revised: 30 Jul 2010

See all articles by Joshua V. Rosenberg

Joshua V. Rosenberg

Federal Reserve Bank of New York

Robert F. Engle

New York University - Leonard N. Stern School of Business - Department of Economics; New York University (NYU) - Department of Finance; National Bureau of Economic Research (NBER)

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Date Written: May 1995

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

Rosenberg, Joshua V. and Engle, Robert F., GARCH Gamma (May 1995). NBER Working Paper No. w5128. Available at SSRN: https://ssrn.com/abstract=225193

Joshua V. Rosenberg

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Robert F. Engle (Contact Author)

New York University - Leonard N. Stern School of Business - Department of Economics ( email )

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New York University (NYU) - Department of Finance

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