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August 1998 Option replication with transaction costs: general diffusion limits
Hyungsok Ahn, Mohit Dayal, Eric Grannan, Glen Swindle
Ann. Appl. Probab. 8(3): 676-707 (August 1998). DOI: 10.1214/aoap/1028903447


Transaction costs preclude the construction of hedging strategies for general contingent claims. Leland introduced the concept of diffusion limits of hedging strategies in a small transaction cost limit. This paper establishes such diffusion limits for very general hedging strategies and also establishes leading order asymptotic expressions for the replication error. In addition to subsuming previously considered temporal strategies, the results in this paper yield new results, namely expressions for replication errors of stock price strategies and a variety of "renewal" strategies. Most importantly, this paper provides a unified methodology for calculating hedging strategies and replication errors in the small transaction cost limit. This is an essential component of optimization methods, when, for example one is trying to minimize replication error for a given initial portfolio value.


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Hyungsok Ahn. Mohit Dayal. Eric Grannan. Glen Swindle. "Option replication with transaction costs: general diffusion limits." Ann. Appl. Probab. 8 (3) 676 - 707, August 1998.


Published: August 1998
First available in Project Euclid: 9 August 2002

zbMATH: 0934.91024
MathSciNet: MR1627760
Digital Object Identifier: 10.1214/aoap/1028903447

Primary: 60G44 , 60H30 , 90A09

Keywords: hedging strategies , Transaction costs

Rights: Copyright © 1998 Institute of Mathematical Statistics


Vol.8 • No. 3 • August 1998
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