Approximate Hedging of Contingent Claims under Transaction Costs for General Pay-offs
AbstractIn 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 InfoArticle provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.
Volume (Year): 17 (2010)
Issue (Month): 6 ()
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Other versions of this item:
- Lépinette-Denis, Emmanuel, 2010. "Approximate Hedging of Contingent Claims Under Transaction Costs for General Pay-Offs," Economics Papers from University Paris Dauphine 123456789/9694, Paris Dauphine University.
- D23 - Microeconomics - - Production and Organizations - - - Organizational Behavior; Transaction Costs; Property Rights
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