GARCH Gamma

JOURNAL OF DERIVATIVES Vol 2 No 4

Posted: 10 Oct 1998

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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Abstract

This article addresses the issue of hedging options positions when the underlying asset exhibits stochastic volatility. By parameterizing the volatility process as GARCH, and utilizing risk-neutral valuation, we approximate hedging parameters (delta and gamma) using Monte Carlo simulation. We estimate hedging parameters for options on the Standard & 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.

JEL Classification: G13

Suggested Citation

Rosenberg, Joshua V. and Engle, Robert F., GARCH Gamma. JOURNAL OF DERIVATIVES Vol 2 No 4. Available at SSRN: https://ssrn.com/abstract=6475

Joshua V. Rosenberg

Federal Reserve Bank of New York ( email )

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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, NY 10003
United States

New York University (NYU) - Department of Finance

Stern School of Business
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New York, NY 10012-1126
United States

National Bureau of Economic Research (NBER)

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