Risk Measure Pricing and Hedging in Incomplete Markets
AbstractThis 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 InfoPaper provided by EconWPA in its series Finance with number 0406004.
Date of creation: 08 Jun 2004
Date of revision: 06 Apr 2005
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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;
Other versions of this item:
- Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January.
- G - Financial Economics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-06-13 (All new papers)
- NEP-CFN-2004-06-13 (Corporate Finance)
- NEP-FIN-2004-06-13 (Finance)
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