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

  • William R. Melick
  • Charles P. Thomas

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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File URL: http://www.federalreserve.gov/pubs/ifdp/1996/541/default.htm
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File URL: http://www.federalreserve.gov/pubs/ifdp/1996/541/ifdp541.pdf
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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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  1. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
  2. 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.
  3. 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.
  4. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
  5. MacKinnon, James G, 1992. "Model Specification Tests and Artificial Regressions," Journal of Economic Literature, American Economic Association, vol. 30(1), pages 102-46, March.
  6. Yacine Aït-Sahalia & Andrew W. Lo, 1998. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," Journal of Finance, American Finance Association, vol. 53(2), pages 499-547, 04.
  7. 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.
  8. 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).
  9. 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.).
  10. 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.
  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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