Local risk-minimization under transaction costs
AbstractWe propose a new approach to the pricing and hedging of contingent claims under transaction costs in a general incomplete market in discrete time. Under the assumptions of a bounded mean-variance tradeoff, substantial risk and a nondegeneracy condition on the conditional variances of asset returns, we prove the existence of a locally risk-minimizing strategy inclusive of transaction costs for every square-integrable contingent claim. Then we show that local riskminimization is robust under the inclusion of transaction costs: The preceding strategy which is locally risk-minimizing inclusive of transaction costs in a model with bid-ask spreads on the underlying asset is also locally risk-minimizing without transaction costs in a fictitious model which is frictionless and where the fictitious asset price lies between the bid and ask price processes of the original model. In particular, our results apply to any nondegenerate model with a finite state space if the transaction cost parameter is sufficiently small. --
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Bibliographic InfoPaper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 1998,18.
Date of creation: 1998
Date of revision:
option pricing; hedging; transaction costs; locally risk-minimizing strategies; mean-variance tradeoff;
Find related papers by JEL classification:
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
- C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
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- Jan Kallsen & Johannes Muhle-Karbe, 2011. "Existence of shadow prices in finite probability spaces," Computational Statistics, Springer, vol. 73(2), pages 251-262, April.
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