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Approximate Hedging of Contingent Claims under Transaction Costs for General Pay-offs

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  • Emmanuel Denis

Abstract

In 1985 Leland suggested an approach to price contingent claims under proportional transaction costs. Its main idea is to use the classical Black-Scholes formula with a suitably enlarged volatility for a periodically revised portfolio whose terminal value approximates the pay-off h(S T) = (S T - K)+ of the call option. In subsequent studies, Lott, Kabanov and Safarian, and Gamys and Kabanov provided a rigorous mathematical analysis and established that the hedging portfolio approximates this pay-off in the case where the transaction costs decrease to zero as the number of revisions tends to infinity. The arguments used heavily the explicit expressions given by the Black-Scholes formula leaving open the problem whether the Leland approach holds for more general options and other types of price processes. In this paper we show that for a large class of the pay-off functions Leland's method can be successfully applied. On the other hand, if the pay-off function h(x) is not convex, then this method does not work.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 17 (2010)
Issue (Month): 6 ()
Pages: 491-518

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Handle: RePEc:taf:apmtfi:v:17:y:2010:i:6:p:491-518

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Keywords: Black-Scholes formula; transaction costs; Leland's strategy; approximate hedging;

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