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May, 1995 There is no Nontrivial Hedging Portfolio for Option Pricing with Transaction Costs
H. M. Soner, S. E. Shreve, J. Cvitanic
Ann. Appl. Probab. 5(2): 327-355 (May, 1995). DOI: 10.1214/aoap/1177004767

Abstract

Conventional wisdom holds that since continuous-time, Black-Scholes hedging is infinitely expensive in a model with proportional transaction costs, there is no continuous-time strategy which hedges a European call option perfectly. Of course, if one is attempting to dominate the European call rather than replicate it, then one can use the trivial strategy of buying one share of the underlying stock and holding to maturity. In this paper we prove that this is, in fact, the least expensive method of dominating a European call in a Black-Scholes model with proportional transaction costs.

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H. M. Soner. S. E. Shreve. J. Cvitanic. "There is no Nontrivial Hedging Portfolio for Option Pricing with Transaction Costs." Ann. Appl. Probab. 5 (2) 327 - 355, May, 1995. https://doi.org/10.1214/aoap/1177004767

Information

Published: May, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0837.90012
MathSciNet: MR1336872
Digital Object Identifier: 10.1214/aoap/1177004767

Subjects:
Primary: 90A09
Secondary: 60H30 , 90A12 , 93E20

Keywords: Black-Scholes portfolio , hedging , option pricing , Transaction costs

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.5 • No. 2 • May, 1995
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