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

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Author Info
John H. Cochrane
Jesus Saa-Requejo

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Abstract

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 National Bureau of Economic Research, Inc in its series NBER Working Papers with number 5489.

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Date of creation: Mar 1996
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Handle: RePEc:nbr:nberwo:5489

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  1. HENROTTE, Philippe, 2002. "Pricing kernels and dynamic portfolios," Les Cahiers de Recherche 768, HEC Paris. [Downloadable!]
  2. Alfredo Ibáñez, 2005. "Option-Pricing in Incomplete Markets: The Hedging Portfolio plus a Risk Premium-Based Recursive Approach," Computing in Economics and Finance 2005 216, Society for Computational Economics. [Downloadable!]
  3. Pierluigi Balduzzi & Cesare Robotti, 2001. "Minimum-variance kernels, economic risk premia, and tests of multi-beta models," Working Paper 2001-24, Federal Reserve Bank of Atlanta. [Downloadable!]
  4. Matos, Joao Amaro de & Lacerda, Ana, 2006. "Dry Markets and Statistical Arbitrage Bounds for European Derivatives," FEUNL Working Paper Series wp479, Universidade Nova de Lisboa, Faculdade de Economia. [Downloadable!]
  5. Björk, Tomas & Slinko, Irina, 2004. "Towards a General Theory of Good Deal Bounds," Working Paper Series in Economics and Finance 595, Stockholm School of Economics. [Downloadable!]
  6. João Amaro de Matos & Paula Antão, 2001. "Super-replicating Bounds on European Option Prices when the Underlying Asset is Illiquid," Economics Bulletin, Economics Bulletin, vol. 7, pages 1-7. [Downloadable!]
  7. Michael Brandt & John Cochrane & Pedro Santa-Clara, 2001. "International Risk Sharing is Better Than You Think (or Exchange Rates are Much Too Smooth!," University of California at Los Angeles, Anderson Graduate School of Management 1015, Anderson Graduate School of Management, UCLA. [Downloadable!]
    Other versions:
  8. Kerkhof, J. & Melenberg, B. & Schumacher, H., 2002. "Model risk and regulatory capital," Discussion Paper 27, Tilburg University, Center for Economic Research. [Downloadable!]
  9. Nicolae Garleanu & Lasse Heje Pedersen & Allen M. Poteshman, 2005. "Demand-Based Option Pricing," NBER Working Papers 11843, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  10. Antonio Bernardo & Olivier Ledoit, 1999. "Approximate Arbitrage," University of California at Los Angeles, Anderson Graduate School of Management 1097, Anderson Graduate School of Management, UCLA. [Downloadable!]
  11. Morten Christensen & Eckhard Platen, 2005. "Sharpe Ratio Maximization and Expected Utility when Asset Prices have Jumps," Research Paper Series 170, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
    Other versions:
  12. David S. Bates, 1999. "Financial Markets' Assessment of EMU," NBER Working Papers 6874, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  13. Matos, Joao Amaro de & Lacerda, Ana, 2004. "Dry Markets and Superreplication Bounds of American Derivatives," FEUNL Working Paper Series wp461, Universidade Nova de Lisboa, Faculdade de Economia. [Downloadable!]
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