Bounding Contingent Claim Prices via Hedging Strategy with Coherent Risk Measures

Bounding Contingent Claim Prices via Hedging Strategy with Coherent Risk Measures

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Article ID: iaor201111158
Volume: 151
Issue: 3
Start Page Number: 613
End Page Number: 632
Publication Date: Dec 2011
Journal: Journal of Optimization Theory and Applications
Authors: , ,
Keywords: optimization, programming: linear, risk
Abstract:

We generalize the notion of arbitrage based on the coherent risk measure, and investigate a mathematical optimization approach for tightening the lower and upper bounds of the price of contingent claims in incomplete markets. Due to the dual representation of coherent risk measures, the lower and upper bounds of price are located by solving a pair of semi‐infinite linear optimization problems, which further reduce to linear optimization when conditional value‐at‐risk (CVaR) is used as risk measure. We also show that the hedging portfolio problem is viewed as a robust optimization problem. Tuning the parameter of the risk measure, we demonstrate by numerical examples that the two bounds approach to each other and converge to a price that is fair in the sense that seller and buyer face the same amount of risk.

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