Risk Measure Pricing and Hedging in Incomplete Markets

Mingxin Xu

Finance from University Library of Munich, Germany

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.

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 (search for similar items in EconPapers)
JEL-codes: G (search for similar items in EconPapers)
Date: 2004-06-08, Revised 2006-03-07
New Economics Papers: this item is included in nep-cfn and nep-fin
Note: Type of Document - pdf
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Related works:
Journal Article: Risk measure pricing and hedging in incomplete markets (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:wpa:wuwpfi:0406004

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