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Using Option Pricing Theory to Infer About Equity Premiums

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  • Aase, Knut K.

    ()
    (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

Abstract

In this paper we make use of option pricing theory to infer about historical equity premiums. This we do by comparing the prices of an American perpetual put option computed using two different models: The first is the standard one with continuous, zero expectation, Gaussian noise, the second is a strikingly similar model, except that the zero expectation noise is of Poissonian type. The interesting fact that makes this comparison worthwhile, is that the probability distribution under the risk adjusted measure turns out to depend on the equity premium in the Poisson model, while this is not so for the standard, Brownian motion version. This difference is utilized to find the intertemporal, equilibrium equity premium. We apply this technique to the US equity data of the last century and find that, if the risk free short rate was around one per cent, this corresponds to a risk premium on equity about two and a half per cent. On the other hand, if the risk free rate was about four per cent, we find that this corresponds to an equity premium of around four and a half per cent. The advantage with our approach is that we only need equity data and option pricing theory, no consumption data was necessary to arrive at these conclusions. We round off the paper by investigating if the procedure also works for incomplete models.

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Bibliographic Info

Paper provided by Department of Business and Management Science, Norwegian School of Economics in its series Discussion Papers with number 2005/11.

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Length: 32 pages
Date of creation: 30 Nov 2005
Date of revision:
Handle: RePEc:hhs:nhhfms:2005_011

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Web page: http://www.nhh.no/en/research-faculty/department-of-business-and-management-science.aspx
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Keywords: Historical equity premiums; perpetual American put option; equity premium puzzle; risk free rate puzzle; geometric Brownian motion; geometric Poisson process; CCAPM;

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References

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  1. Rietz, Thomas A., 1988. "The equity risk premium a solution," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 117-131, July.
  2. Philippe Weil, 1989. "The Equity Premium Puzzle and the Riskfree Rate Puzzle," NBER Working Papers 2829, National Bureau of Economic Research, Inc.
  3. Bick, Avi, 1987. "On the Consistency of the Black-Scholes Model with a General Equilibrium Framework," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(03), pages 259-275, September.
  4. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  5. Campbell, John, 1996. "Understanding Risk and Return," Scholarly Articles 3153293, Harvard University Department of Economics.
  6. John Y. Campbell, 1992. "Intertemporal Asset Pricing Without Consumption Data," NBER Working Papers 3989, National Bureau of Economic Research, Inc.
  7. Jan Ubøe & Bernt Øksendal & Knut Aase & Nicolas Privault, 2000. "White noise generalizations of the Clark-Haussmann-Ocone theorem with application to mathematical finance," Finance and Stochastics, Springer, vol. 4(4), pages 465-496.
  8. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  9. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
  10. Ellen R. McGrattan & Edward C. Prescott, 2003. "Average debt and equity returns: puzzling?," Staff Report 313, Federal Reserve Bank of Minneapolis.
  11. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  12. Knut K. Aase, 2002. "Equilibrium Pricing in the Presence of Cumulative Dividends Following a Diffusion," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 173-198.
  13. Constantinides, George M, 1990. "Habit Formation: A Resolution of the Equity Premium Puzzle," Journal of Political Economy, University of Chicago Press, vol. 98(3), pages 519-43, June.
  14. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
  15. Knut Aase, 1999. "An Equilibrium Model of Catastrophe Insurance Futures and Spreads," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 24(1), pages 69-96, June.
  16. Aase, Knut K., 2005. "The perpetual American put option for jump-diffusions with applications," Discussion Papers 2005/12, Department of Business and Management Science, Norwegian School of Economics.
  17. Mehra, Rajnish & Prescott, Edward C., 1988. "The equity risk premium: A solution?," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 133-136, July.
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