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Risk measure pricing and hedging in incomplete markets

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  • Mingxin Xu

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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

Article provided by Springer in its journal Annals of Finance.

Volume (Year): 2 (2006)
Issue (Month): 1 (January)
Pages: 51-71

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Handle: RePEc:kap:annfin:v:2:y:2006:i:1:p:51-71

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Web page: http://www.springerlink.com/link.asp?id=112370

Related research

Keywords: Derivative pricing; Valuation 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; Risk indifference pricing; C60; D46; G13;

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Citations

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Cited by:
  1. 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.
  2. Takuji Arai & Masaaki Fukasawa, 2011. "Convex risk measures for good deal bounds," Papers 1108.1273, arXiv.org.
  3. Michail Anthropelos, 2012. "Agents' Strategic Behavior in Optimal Risk Sharing," Papers 1206.0384, arXiv.org, revised Mar 2013.
  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. 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.
  7. Mustafa Pınar, 2011. "Gain–loss based convex risk limits in discrete-time trading," Computational Management Science, Springer, vol. 8(3), pages 299-321, August.

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