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Optimal design of derivatives in illiquid markets

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  • Pauline Barrieu
  • Nicole El Karoui

Abstract

The aim of this paper is to determine the optimal structure of derivatives written on an illiquid asset, such as a catastrophic or a weather event. This transaction involves two agents: a bank which wants to hedge its initial exposure towards this illiquid asset and an investor which may buy the contract. Both agents also have the opportunity to invest their residual wealth on a financial market. Based on a utility maximization point of view, we determine an optimal profile (and its value) such that it maximizes the bank's utility given that the investor decides to make the deal only if it increases its utility. In the case of exponential utility, we show that the pricing rule is a non-linear function of the structure and that the bank always transfers the same proportion of its initial exposure. In the general case, an additional term appears, depending only on the relative log-likelihood of the two agents' views of the distribution of the illiquid asset.

Suggested Citation

  • Pauline Barrieu & Nicole El Karoui, 2002. "Optimal design of derivatives in illiquid markets," Quantitative Finance, Taylor & Francis Journals, vol. 2(3), pages 181-188.
  • Handle: RePEc:taf:quantf:v:2:y:2002:i:3:p:181-188 DOI: 10.1088/1469-7688/2/3/301
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    References listed on IDEAS

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    1. Prema-chandra Athukorala & Satish Chand, 1998. "Trade Orientation and Productivity Gains from International Production: A Study of Overseas Operations of US Multinationals," Departmental Working Papers 1998-02, The Australian National University, Arndt-Corden Department of Economics.
    2. Merton H. Miller & Franco Modigliani, 1961. "Dividend Policy, Growth, and the Valuation of Shares," The Journal of Business, University of Chicago Press, vol. 34, pages 411-411.
    3. A. C. Miller, 1902. "Fiscal Reciprocity," Journal of Political Economy, University of Chicago Press, vol. 10, pages 255-255.
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    Cited by:

    1. El-Karoui, N. & Hamadène, S., 2003. "BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 145-169, September.
    2. Dana, Rose-Anne & Scarsini, Marco, 2007. "Optimal risk sharing with background risk," Journal of Economic Theory, Elsevier, pages 152-176.
    3. Monoyios, Michael, 2004. "Option pricing with transaction costs using a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 889-913, February.
    4. repec:dau:papers:123456789/698 is not listed on IDEAS

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