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Incomplete markets, transaction costs and liquidity effects

Author

Listed:
  • E. Jouini
  • P. -F. Koehl
  • N. Touzi

Abstract

An agent's optimization problem of the expected terminal wealth utility in a trinomial tree economy is solved. At each transaction date, the agent can trade in a riskless asset, a primitive asset subject to constant proportional transaction costs, and a contingent claim characterized by some parameter kappa whose bid and ask price is defined by allowing for different equivalent martingale measures. In addition to the classical portfolio choice problem, the characteristic of the contingent claim κ is determined endogenously in the optimization problem. Under suitable conditions, it is proved that the optimal demand of the agent in the primitive risky asset is zero independently of the choice of the terminal wealth utility function: the agent prefers not to trade in the asset subject to transaction costs, which prevents the market from being complete, rather than trading in both assets. Next, the optimal choice of the contingent claim is characterized and the results are applied to European call and put options with fixed maturity and varying exercise price κ.

Suggested Citation

  • E. Jouini & P. -F. Koehl & N. Touzi, 1997. "Incomplete markets, transaction costs and liquidity effects," The European Journal of Finance, Taylor & Francis Journals, vol. 3(4), pages 325-347.
  • Handle: RePEc:taf:eurjfi:v:3:y:1997:i:4:p:325-347
    DOI: 10.1080/135184797337408
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    References listed on IDEAS

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    1. Darrell Duffie & Chi-Fu Huang, 2005. "Implementing Arrow-Debreu Equilibria By Continuous Trading Of Few Long-Lived Securities," World Scientific Book Chapters,in: Theory Of Valuation, chapter 4, pages 97-127 World Scientific Publishing Co. Pte. Ltd..
    2. Isabelle Bajeux-Besnainou & Jean-Charles Rochet, 1996. "Dynamic Spanning: Are Options An Appropriate Instrument?," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 1-16.
    3. Duffie Darrell & Rahi Rohit, 1995. "Financial Market Innovation and Security Design: An Introduction," Journal of Economic Theory, Elsevier, vol. 65(1), pages 1-42, February.
    4. Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, Oxford University Press, vol. 90(1), pages 75-89.
    5. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    6. repec:dau:papers:123456789/5630 is not listed on IDEAS
    7. Bernard Bensaid & Jean-Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86.
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