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Using options prices to infer PDF'S for asset prices: an application to oil prices during the Gulf crisis

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  • William R. Melick
  • Charles P. Thomas

Abstract

We develop a general method to infer martingale equivalent probability density functions (PDFs) for asset prices using American options prices. The early exercise feature of American options precludes expressing the option price in terms of the PDF of the price of the underlying asset. We derive tight bounds for the option price in terms of the PDF and demonstrate how these bounds, together with observed option prices, can be used to estimate the parameters of the PDF. We infer the distribution for the price of crude oil during the Persian Gulf crisis and find the distribution differs significantly from that recovered using standard techniques.

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Bibliographic Info

Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series International Finance Discussion Papers with number 541.

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Date of creation: 1996
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Handle: RePEc:fip:fedgif:541

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Related research

Keywords: Power resources - Prices ; Options (Finance) ; Persian Gulf War; 1991;

References

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  1. Perrakis, Stylianos & Ryan, Peter J, 1984. " Option Pricing Bounds in Discrete Time," Journal of Finance, American Finance Association, vol. 39(2), pages 519-25, June.
  2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  3. Yacine Ait-Sahalia & Andrew W. Lo, 1995. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," NBER Working Papers 5351, National Bureau of Economic Research, Inc.
  4. Lo, Andrew W., 1987. "Semi-parametric upper bounds for option prices and expected payoffs," Journal of Financial Economics, Elsevier, vol. 19(2), pages 373-387, December.
  5. Levy, Haim, 1985. " Upper and Lower Bounds of Put and Call Option Value: Stochastic Dominance Approach," Journal of Finance, American Finance Association, vol. 40(4), pages 1197-1217, September.
  6. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
  7. MacKinnon, James G, 1992. "Model Specification Tests and Artificial Regressions," Journal of Economic Literature, American Economic Association, vol. 30(1), pages 102-46, March.
  8. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
  9. James A. Overdahl & H. Lee Matthews, 1988. "The Use of NYMEX Options to Forecast Crude Oil Prices," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4).
  10. William R. Melick & Charles P. Thomas, 1992. "War and peace: recovering the market's probability distribution of crude oil futures prices during the Gulf crisis," International Finance Discussion Papers 437, Board of Governors of the Federal Reserve System (U.S.).
  11. Ritchey, Robert J, 1990. "Call Option Valuation for Discrete Normal Mixtures," Journal of Financial Research, Southern Finance Association & Southwestern Finance Association, vol. 13(4), pages 285-96, Winter.
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Citations

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Cited by:
  1. Campa, Jose Manuel & Chang, P. H. Kevin, 1998. "The forecasting ability of correlations implied in foreign exchange options," Journal of International Money and Finance, Elsevier, vol. 17(6), pages 855-880, December.
  2. Bank for International Settlements, 2002. "Central bank intervention and market expectations," BIS Papers, Bank for International Settlements, number 10, May.
  3. Bronka Rzepkowski, 2000. "The Expectations of Hong Kong Dollar Devaluation and Their Determinants," Working Papers 2000-04, CEPII research center.
  4. Sheri Markose & Amadeo Alentorn, 2005. "Option Pricing and the Implied Tail Index with the Generalized Extreme Value (GEV) Distribution," Computing in Economics and Finance 2005 397, Society for Computational Economics.
  5. Michael P. Leahy & Charles P. Thomas, 1996. "The sovereignty option: the Quebec referendum and market views on the Canadian dollar," International Finance Discussion Papers 555, Board of Governors of the Federal Reserve System (U.S.).
  6. Bronka Rzepkowski, 2001. "Heterogeneous Expectations, Currency Options and the Euro / Dollar Exchange Rate," Working Papers 2001-03, CEPII research center.
  7. Sheri Markose & Amadeo Alentorn, 2005. "The Generalized Extreme Value (GEV) Distribution, Implied Tail Index and Option Pricing," Economics Discussion Papers 594, University of Essex, Department of Economics.
  8. Amadeo Alentorn & Sheri Markose, 2006. "Removing Maturity Effects of Implied Risk Neutral Densities and Related Statistics," Economics Discussion Papers 609, University of Essex, Department of Economics.

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