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

  • John H. Cochrane
  • Jesus Saa-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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File URL: http://dx.doi.org/10.1086/262112
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Article provided by University of Chicago Press in its journal Journal of Political Economy.

Volume (Year): 108 (2000)
Issue (Month): 1 (February)
Pages: 79-119

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Handle: RePEc:ucp:jpolec:v:108:y:2001:i:1:p:79-119
Contact details of provider: Web page: http://www.journals.uchicago.edu/JPE/

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  1. Ritchken, Peter H, 1985. " On Option Pricing Bounds," Journal of Finance, American Finance Association, vol. 40(4), pages 1219-33, September.
  2. Hua He and Neil D. Pearson., 1989. "Consumption and Portfolio Policies with Incomplete Markets and Short-Sale Constraints: The Infinite Dimensional Case," Research Program in Finance Working Papers RPF-191, University of California at Berkeley.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. Hayne E. Leland., 1984. "Option Pricing and Replication with Transactions Costs," Research Program in Finance Working Papers 144, University of California at Berkeley.
  8. 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.
  9. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474, 06-2016.
  10. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  11. 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.
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