Hedging Options in a GARCH Environment: Testing the Term Structure of Stochastic Volatility Models

36 Pages Posted: 5 Sep 2000 Last revised: 29 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)

Date Written: December 1994

Abstract

This paper develops a methodology for testing the term structure of volatility forecasts derived from stochastic volatility models, and implements it to analyze models of S&P 500 index volatility. Volatility models are compared by their ability to hedge options positions sensitive to the term structure of volatility. Overall, the most effective hedge is a Black-Scholes (BS) delta-gamma hedge, while the BS delta-vega hedge is the least effective. The most successful volatility hedge is GARCH components delta-gamma, suggesting that the GARCH components estimate of the term structure of volatility is most accurate. The success of the BS delta-gamma hedge may be due to mispricing in the options market over the sample period.

Suggested Citation

Rosenberg, Joshua V. and Engle, Robert F., Hedging Options in a GARCH Environment: Testing the Term Structure of Stochastic Volatility Models (December 1994). NBER Working Paper No. w4958. Available at SSRN: https://ssrn.com/abstract=226557

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 University (NYU) - Department of Finance

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