Local risk-minimization under transaction costs

Damien Lamberton, Huyên Pham and Martin Schweizer

No 1998,18, SFB 373 Discussion Papers from Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes

Abstract: We 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.

Keywords: option pricing; hedging; transaction costs; locally risk-minimizing strategies; mean-variance tradeoff (search for similar items in EconPapers)
JEL-codes: C60 G10 (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (15)

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Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb373:199818

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