Option Hedging Using Empirical Pricing Kernels

35 Pages Posted: 16 Jul 2000 Last revised: 6 Oct 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)

Multiple version iconThere are 2 versions of this paper

Date Written: October 1997

Abstract

This paper develops a method for option hedging which is consistent with time-varying preferences and probabilities. The preferences are expressed in the form of an empirical pricing kernel (EPK), which measures the state price per unit probability, while probabilities are derived from an estimated stochastic volatility model of the form GARCH components with leverage. State prices are estimated using the flexible risk-neutral density method of Rosenberg (1995) and a daily cross-section of option premia. Time-varying preferences over states are linked to a dynamic model of the underlying price to obtain a one-day ahead forecast of derivative price distributions and minimum variance hedge ratios. Empirical results suggest that risk aversion over S&P500 return states is substantially higher than risk aversion implied by Black-Scholes state prices and probabilities using long run estimates of S&P500 return moments. It is also found that the daily level of risk aversion is strongly positively autocorrelated, negatively correlated with S&P500 price changes,and positively correlated with the spread between implied and objective volatilities. Hedging results reveal that typical hedging techniques for out-of-the-money S&P500 index options, such as Black-Scholes or historical minimum variance hedging, are inferior to the EPK hedging method. Thus, time-varying preferences and probabilities appear to be an important factor in the day-to-day pricing of S&P500 options.

Suggested Citation

Rosenberg, Joshua V. and Engle, Robert F., Option Hedging Using Empirical Pricing Kernels (October 1997). NBER Working Paper No. w6222. Available at SSRN: https://ssrn.com/abstract=225980

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Robert F. Engle

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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