The Theory of Good-Deal Pricing in Financial Markets

  • Aleš Černý
  • Stewart Hodges
Part of the Springer Finance book series (FINANCE)


The term ‘no-good-deal pricing’ in this paper encompasses pricing techniques base on the absence of attractive investment opportunities — good deals — in equilibrium. We borrowed the term from [8] who pioneered the calculation of price bands conditional on the absence of high Sharpe Ratios. Alternative methodologies for calculating tighter-than-no-arbitrage price bounds have been suggested by [4], [6], [12]. The theory presented here shows that any of these techniques can be seen as a generalization of no-arbitrage pricing. The common structure is provided by the Extension and Pricing Theorems, already well known from no-arbitrage pricing, see [15]. We derive these theorems in no-good-deal framework and establish general properties of no-good-deal prices. These abstract results are then applied to no-goos-deal bounds determined by von Neumann-Morgenstern preferences in a finite state model1. One important result is that no-good-deal bouns generated by an unbounded utility function are always strictly tighter than the no-arbitrage bounds. The same is not true for bounded utility functions. For smooth utility functions we show that one will obtain the no-arbitrage and the representative agent equilibrium as the two opposite ends of a spectrum of no-good-deal equilibrium restrictions indexed by the maximum attainable certainty equivalent gains.


Good Deal Sharpe Ratio Complete Market Basis Asset Positive Claim 
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  1. 1.
    Philippe Artzner, Freddy Delbaen, Jean-Marc Eber, and David Heath. Coherent measures of risk. Mathematical Finance, 9 (3): 203–228, 1999.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Brian Beavis and Ian Dobbs. Optimization and Stability Theory or Economic Analysis. Cambridge University Press, 1990.Google Scholar
  3. 3.
    Fabio Bellini and Marco Fritelli. On the existence of minimax martingale measures. Rapporto di Ricerca 14/2000, University degli Studi Milano - Bicocca, May 2000.Google Scholar
  4. 4.
    Antonio Bernardo and Olivier Ledoit. Gain, loss and asset pricing. Journal of Political Economy, 108 (1): 144–172, 2000.CrossRefGoogle Scholar
  5. 5.
    Antonio E. Bernardo and Olivier Ledoit. Approximate arbitrage. Working paper 18–99, Anderson School,, November 1999.Google Scholar
  6. 6.
    Aleš Cerný. Generalized Sharpe Ratio and consistent good-deal restrictions in a model of continuous trading. Discussion Paper SWP9902, Imperial College Management School, April 1999.Google Scholar
  7. 7.
    Stephen A. Clark.T he valuation problem in arbitrage price theory. Journal of Mathematical Economics, 22: 463–478, 1993.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    John H. Cochrane and Jesus Sad-equejo. Beyond arbitrage: Good-Ddeal asset price bounds in incomplete markets. Journal of Molitical Economy, 108 (1): 79–119, 2000.CrossRefGoogle Scholar
  9. 9.
    Philip H. Dybvig and Stephen A. Ross. Arbitrage. In J. Eatwell,M.M ilgate, and P. Newman, editors, The New Palgrave: A Dictionary o Economics, volume 1, pages 100–106. M acmillan, London, 1987.Google Scholar
  10. 10.
    Nicole El Karoui and Marie-Claire Quenez. Dynamic programming and pricing of contingent claims in an incomplete market. Journal of Control and Optimization, 33 (1): 29–66, 1995.CrossRefzbMATHGoogle Scholar
  11. 11.
    Lars Peter Hansen and Ravi Jagannathan. Implications of security market data for models of dynamic economies. Journal of Political Economy, 99 (2): 225–262, 1991.CrossRefGoogle Scholar
  12. 12.
    Stewart odges. A generalization of the Sharpe atio and its application to valuation bounds and risk measures. FORC reprint 9888, niversity of arwick, pril 1998.Google Scholar
  13. 13.
    Jonathan E. Ingersoll. Theory of Financial Decision Making. Rowman, and Littleeld Studies in Financial Economics. Rowman, and Littleeld, 1987.Google Scholar
  14. 14.
    Stefan Jaschke and UweK uechler. Coherent risk measures and good-deal bounds.F inance and Stochastics, 5(2), 2001.Google Scholar
  15. 15.
    D.Kreps. Arbitrage and equilibrium in economies with innitely many commodities. Journal of Mathematical Economics, 8: 15–35, 1981.MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Robert Merton. Theory of rational option pricing. Bell Journal o Economics and Management Science, 4: 141–183, 1973.CrossRefGoogle Scholar
  17. 16.
    Peter H. Ritchken. On option pricing bounds. The Journal o Finance, 40 (4): 1219–1233, 1985.CrossRefGoogle Scholar
  18. 18.
    Stephen A.R oss. The arbitrage theory of capital asset pricing. Journal of aconomic theory, 13: 341–360, 1976.CrossRefGoogle Scholar
  19. 19.
    Stephen A. Ross. A simple approach to the valuation of risky streams. Journal of Business, 51: 453–475, 1978.MathSciNetCrossRefGoogle Scholar
  20. 20.
    Mark Rubinstein. The valuation of uncertain income streams and the pricing of options. The Bell Journal of Economics, 7: 407–425, 1976.CrossRefGoogle Scholar
  21. 21.
    Walter Schachermayer. Martingale measures for discrete time processes with innite horizon. Mathematical Finance, 4 (1): 25–55, 1994.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Aleš Černý
    • 1
  • Stewart Hodges
    • 1
  1. 1.Imperial College Management School Financial Options Research CentreUniversity of WarwickUK

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