The Annals of Applied Probability

There is no Nontrivial Hedging Portfolio for Option Pricing with Transaction Costs

H. M. Soner, S. E. Shreve, and J. Cvitanic

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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.

Article information

Source
Ann. Appl. Probab. Volume 5, Number 2 (1995), 327-355.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1177004767

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aoap/1177004767

Mathematical Reviews number (MathSciNet)
MR1336872

Zentralblatt MATH identifier
0837.90012

Subjects
Primary: 90A09
Secondary: 90A12 60H30: Applications of stochastic analysis (to PDE, etc.) 93E20: Optimal stochastic control

Keywords
Transaction costs hedging option pricing Black-Scholes portfolio

Citation

Soner, H. M.; Shreve, S. E.; Cvitanic, J. There is no Nontrivial Hedging Portfolio for Option Pricing with Transaction Costs. The Annals of Applied Probability 5 (1995), no. 2, 327--355. doi:10.1214/aoap/1177004767. http://projecteuclid.org/euclid.aoap/1177004767.


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