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Beyond Arbitrage: "Good-Deal" Asset Price Bounds in Incomplete Markets

  • JOHN H. COCHRANE
  • JESÚS SAÁ-REQUEJO

It is often useful to price assets and other random payoffs by reference to other observed prices rather than construct full-fledged economic asset pricing models. This approach breaks down if one cannot find a perfect replicating portfolio. We impose weak economic restrictions to derive usefully tight bounds on asset prices in this situation. The bounds basically rule out high Sharpe ratios - `good deals' - as well as arbitrage opportunities. We present the method of calculation, we extend it to a multiperiod context by finding a recursive solution, and we apply it to option pricing examples including the Black-Scholes setup with infrequent trading, and a model with stochastic stock volatility and a varying riskfree rate.

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Paper provided by Center for Research in Security Prices, Graduate School of Business, University of Chicago in its series CRSP working papers with number 430.

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Date of creation: Jan 1998
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Handle: RePEc:wop:chispw:430
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  1. Hua He and Neil D. Pearson., 1989. "Consumption and Portfolio Policies with Incomplete Markets and Short-Sale Constraints: The Finite Dimensional Case," Research Program in Finance Working Papers RPF-189, University of California at Berkeley.
  2. Shmuel Kandel & Robert F. Stambaugh, 1994. "Portfolio Inefficiency and the Cross-Section of Expected Returns," NBER Working Papers 4702, National Bureau of Economic Research, Inc.
  3. 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.
  4. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474, 06-2016.
  5. Hayne E. Leland., 1984. "Option Pricing and Replication with Transactions Costs," Research Program in Finance Working Papers 144, University of California at Berkeley.
  6. Ritchken, Peter H, 1985. " On Option Pricing Bounds," Journal of Finance, American Finance Association, vol. 40(4), pages 1219-33, September.
  7. Lars Peter Hansen & John Heaton & Erzo Luttmer, 1993. "Econometric Evaluation of Asset Pricing Models," NBER Technical Working Papers 0145, National Bureau of Economic Research, Inc.
  8. MacKinlay, A. Craig, 1995. "Multifactor models do not explain deviations from the CAPM," Journal of Financial Economics, Elsevier, vol. 38(1), pages 3-28, May.
  9. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
  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. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
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