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Utility based pricing of contingent claims in incomplete markets

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  • Andrea Gam
  • Paolo Pellizzari

Abstract

In a discrete setting, a model is developed for pricing a contingent claim in incomplete markets. Since hedging opportunities influence the price of a contingent claim, the optimal hedging strategy is first introduced assuming that a contingent claim has been issued: a strategy implemented by investing initial wealth plus the selling price is optimal if it maximizes the expected utility of the agent's net payoff, which is the difference between the outcome of the hedging portfolio and the payoff of the claim. The 'reservation price' is then introduced as a subjective valuation of a contingent claim. This is defined as the minimum price that makes the issue of the claim preferable to staying put given that, once the claim has been written, the writer hedges it according to the expected utility criterion. The reservation price is defined both for a short position (reservation selling price) and for a long position (reservation buying price) in the claim. When the contingent claim is redundant, both the selling and the buying price collapse in the usual Arrow-Debreu (or Black-Scholes) price. If the claim is non-redundant, then the reservation prices are interior points of the bid-ask interval. Two numerical examples are provided with different utility functions and contingent claims. Some qualitative properties of the reservation price are shown.

Suggested Citation

  • Andrea Gam & Paolo Pellizzari, 2002. "Utility based pricing of contingent claims in incomplete markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(4), pages 241-260.
    • Handle: RePEc:taf:apmtfi:v:9:y:2002:i:4:p:241-260
    DOI: 10.1080/1350486021000029255
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    References listed on IDEAS

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    1. Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(1), pages 1-12, March.
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    Cited by:

    1. Lampros Boukas & Diogo Pinheiro & Alberto Pinto & Stylianos Xanthopoulos & Athanasios Yannacopoulos, 2009. "Behavioural and Dynamical Scenarios for Contingent Claims Valuation in Incomplete Markets," Papers 0903.3657, arXiv.org.
    2. Fang, Mingyu & Tan, Ken Seng & Wirjanto, Tony S., 2024. "Valuation of carbon emission allowance options under an open trading phase," Energy Economics, Elsevier, vol. 131(C).

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