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Risk Measure Pricing and Hedging in Incomplete Markets

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  • Mingxin Xu

    (University of North Carolina at Charlotte)

Abstract

This article attempts to extend the complete market option pricing theory to incomplete markets. Instead of eliminating the risk by a perfect hedging portfolio, partial hedging will be adopted and some residual risk at expiration will be tolerated. The risk measure (or risk indifference) prices charged for buying or selling an option are associated to the capital required for dynamic hedging so that the risk exposure will not increase. The associated optimal hedging portfolio is decided by minimizing a convex measure of risk. We will give the definition of risk-efficient options and confirm that options evaluated by risk measure pricing rules are indeed risk-efficient. Relationships to utility indifference pricing and pricing by valuation and stress measures proposed in Carr et al. (2001) will be discussed. Examples using shortfall risk measure and average VaR will be discussed.

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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 0406004.

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Date of creation: 08 Jun 2004
Date of revision: 06 Apr 2005
Handle: RePEc:wpa:wuwpfi:0406004

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Web page: http://128.118.178.162

Related research

Keywords: Pricing and Hedging; Incomplete Markets; Dynamic Shortfall Risk; Average Value at Risk; Utility Indifference Pricing; Convex Measure of Risk; Coherent Risk Measure; Risk-Efficient Options; Semimartingale Models;

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References

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  1. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
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Citations

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Cited by:
  1. Takuji Arai & Masaaki Fukasawa, 2011. "Convex risk measures for good deal bounds," Papers 1108.1273, arXiv.org.
  2. Michail Anthropelos & Gordan Žitković, 2010. "Partial equilibria with convex capital requirements: existence, uniqueness and stability," Annals of Finance, Springer, vol. 6(1), pages 107-135, January.
  3. Michail Anthropelos & Nikolaos E. Frangos & Stylianos Z. Xanthopoulos & Athanasios N. Yannacopoulos, 2008. "On contingent claims pricing in incomplete markets: A risk sharing approach," Papers 0809.4781, arXiv.org, revised Feb 2012.
  4. Michail Anthropelos & Gordan Zitkovic, 2009. "Partial Equilibria with Convex Capital Requirements: Existence, Uniqueness and Stability," Papers 0901.3318, arXiv.org.
  5. Pascal François & Geneviève Gauthier & Frédéric Godin, 2012. "Optimal Hedging when the Underlying Asset Follows a Regime-switching Markov Process," Cahiers de recherche 1234, CIRPEE.
  6. Mustafa Pınar, 2011. "Gain–loss based convex risk limits in discrete-time trading," Computational Management Science, Springer, vol. 8(3), pages 299-321, August.
  7. Michail Anthropelos, 2012. "Agents' Strategic Behavior in Optimal Risk Sharing," Papers 1206.0384, arXiv.org, revised Mar 2013.

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