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The Influence of Heterogeneous Preferences on Asset Prices in an Incomplete Market Model

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  • Frank Niehaus

    (University of Hannover)

Abstract

In this paper, we examine an exchange economy with a financial market composed of three assets: shares of a stock, European call options written on the stock, and riskless bonds. The financial market is assumed to be incomplete and the option is not a redundant asset. In such a case the construction of a riskless hedge-portfolio to valuate the option is unfeasible and therefore the pricing of the assets becomes a simultaneous valuation problem, nonlineary depending on the preferences of the agents. First, the case of homogeneous agents (or equivalently of a representative agent) is studied. By means of numerical analysis, it can be found that individual preferences have a major impact on the price relation of the assets, including the price of the option. This stays in contrast to the Black-Scholes analysis, where the option is a redundant asset. A unique price relation exists and no trading takes place. In the case of heterogeneous agents the price relation of the assets crucially depends on the span of the heterogeneity of the preferences. Now, trading takes place. The more risk averse agents buy the bond and sell the share and the option, whereas the less risk averse agents buy the option and the share and sell the riskless bond. More surprisingly we find that the representative asset-pricing-model overprices the riskless bond and underprices the option in relation to our model of heterogeneous agents.

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Bibliographic Info

Paper provided by Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance in its series CeNDEF Workshop Papers, January 2001 with number 2A.2.

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Date of creation: 04 Jan 2001
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Handle: RePEc:ams:cdws01:2a.2

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Keywords: Asset pricing; Incomplete markets; Option pricing; Heterogeneous agents;

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References

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  1. Rubinstein, Mark, 1974. "An aggregation theorem for securities markets," Journal of Financial Economics, Elsevier, vol. 1(3), pages 225-244, September.
  2. Franke, Gunter & Stapleton, Richard C. & Subrahmanyam, Marti G., 1998. "Who Buys and Who Sells Options: The Role of Options in an Economy with Background Risk," Journal of Economic Theory, Elsevier, vol. 82(1), pages 89-109, September.
  3. Detemple, Jerome B & Selden, Larry, 1991. "A General Equilibrium Analysis of Option and Stock Market Interactions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(2), pages 279-303, May.
  4. Guenter Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "When are Options Overpriced? The Black-Scholes Model and Alternative Characterisations of the Pricing Kernel," CoFE Discussion Paper 99-01, Center of Finance and Econometrics, University of Konstanz.
  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. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  7. Guenter Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "When are Options Overpriced? The Black-Scholes Model and Alternative Characterisations of the Pricing Kernel," Finance 9904004, EconWPA.
  8. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
  9. Bailey, Warren & Stulz, René M., 1989. "The Pricing of Stock Index Options in a General Equilibrium Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(01), pages 1-12, March.
  10. Leland, Hayne E, 1980. " Who Should Buy Portfolio Insurance?," Journal of Finance, American Finance Association, vol. 35(2), pages 581-94, May.
  11. Dietmar P.J. Leisen and Kenneth L. Judd, 2001. "A Partial Equilibrium Model of Option Markets," Computing in Economics and Finance 2001 219, Society for Computational Economics.
  12. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
  13. Drees, Burkhard & Eckwert, Bernhard, 1995. " The Risk and Price Volatility of Stock Options in General Equilibrium," Scandinavian Journal of Economics, Wiley Blackwell, vol. 97(3), pages 459-67, September.
  14. Brennan, M J, 1979. "The Pricing of Contingent Claims in Discrete Time Models," Journal of Finance, American Finance Association, vol. 34(1), pages 53-68, March.
  15. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  16. Mark Rubinstein, 1976. "The Valuation of Uncertain Income Streams and the Pricing of Options," Bell Journal of Economics, The RAND Corporation, vol. 7(2), pages 407-425, Autumn.
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Cited by:
  1. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
  2. Sabrina Ecca & Michele Marchesi & Alessio Setzu, 2008. "Modeling and Simulation of an Artificial Stock Option Market," Computational Economics, Society for Computational Economics, vol. 32(1), pages 37-53, September.

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