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Option Hedging Using Empirical Pricing Kernels

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  • Joshua V. Rosenberg
  • Robert F. Engle

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.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 6222.

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Date of creation: Oct 1997
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Publication status: published as Rosenberg, Joshua V. and Robert F. Engle. "Empirical Pricing Kernels," Journal of Financial Economics, 2002, v64(3,Jun), 341-372.
Handle: RePEc:nbr:nberwo:6222

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References

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  1. Lars Peter Hansen & Ravi Jagannathan, 1990. "Implications of security market data for models of dynamic economies," Discussion Paper / Institute for Empirical Macroeconomics 29, Federal Reserve Bank of Minneapolis.
  2. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
  3. Stapleton, Richard C & Subrahmanyam, Marti G, 1984. " The Valuation of Options When Asset Returns Are Generated by a Binomial Process," Journal of Finance, American Finance Association, vol. 39(5), pages 1525-39, December.
  4. Russell P. Robins & Barry Schachter, 1994. "An Analysis of the Risk in Discretely Rebalanced Option Hedges and Delta-Based Techniques," Management Science, INFORMS, vol. 40(6), pages 798-808, June.
  5. Hansen, Lars Peter & Singleton, Kenneth J, 1983. "Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 249-65, April.
  6. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1996. "Implied Volatility Functions: Empirical Tests," NBER Working Papers 5500, National Bureau of Economic Research, Inc.
  7. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-86, September.
  8. Rosenberg, Joshua V., 1998. "Pricing multivariate contingent claims using estimated risk-neutral density functions," Journal of International Money and Finance, Elsevier, vol. 17(2), pages 229-247, April.
  9. Dumas, Bernard J & Fleming, Jeff & Whaley, Robert E, 1996. "Implied Volatility Functions: Empirical Tests," CEPR Discussion Papers 1369, C.E.P.R. Discussion Papers.
  10. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
  11. Gallant, A. Ronald & Hansen, Lars Peter & Tauchen, George, 1990. "Using conditional moments of asset payoffs to infer the volatility of intertemporal marginal rates of substitution," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 141-179.
  12. John H. Cochrane & Lars Peter Hansen, 1992. "Asset Pricing Explorations for Macroeconomics," NBER Chapters, in: NBER Macroeconomics Annual 1992, Volume 7, pages 115-182 National Bureau of Economic Research, Inc.
  13. Brennan, M J, 1979. "The Pricing of Contingent Claims in Discrete Time Models," Journal of Finance, American Finance Association, vol. 34(1), pages 53-68, March.
  14. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October.
  15. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
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Citations

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Cited by:
  1. Allan Timmermann & Massimo Guidolin, 2001. "Option Prices under Bayesian Learning: Implied Volatility Dynamics and Predictive Densities," FMG Discussion Papers dp397, Financial Markets Group.
  2. Jens Carsten Jackwerth, 1998. "Recovering Risk Aversion from Option Prices and Realized Returns," Finance 9803002, EconWPA.
  3. Lim, G.C. & Martin, G.M. & Martin, V.L., 2006. "Pricing currency options in the presence of time-varying volatility and non-normalities," Journal of Multinational Financial Management, Elsevier, vol. 16(3), pages 291-314, July.
  4. V. L. Martin & G. M. Martin & G. C. Lim, 2005. "Parametric pricing of higher order moments in S&P500 options," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(3), pages 377-404.

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