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A closed-form solution to the problem of super-replication under transaction costs

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Author Info
HuyËn Pham () (Equipe d'Analyse et de MathÊmatiques AppliquÊes, UniversitÊ Marne-la-VallÊe, F-77454 Marne-la-VallÊe Cedex 2, France and CREST)
Nizar Touzi () (CEREMADE, UniversitÊ Paris Dauphine, F-75775 Paris Cedex, France and CREST Manuscript)
Jaksa Cvitanic () (Department of Statistics, Columbia University, New York, NY 10027, USA)

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Abstract

We study the problem of finding the minimal price needed to dominate European-type contingent claims under proportional transaction costs in a continuous-time diffusion model. The result we prove has already been known in special cases - the minimal super-replicating strategy is the least expensive buy-and-hold strategy. Our contribution consists in showing that this result remains valid for general path-independent claims, and in providing a shorter and more intuitive, financial mathematics-type proof. It is based on a previously known representation of the minimal price as a supremum of the prices in corresponding shadow markets, and on a PDE (viscosity) characterization of that representation.

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Publisher Info
Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 3 (1999)
Issue (Month): 1 ()
Pages: 35-54
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Handle: RePEc:spr:finsto:v:3:y:1999:i:1:p:35-54

Note: received: May 1997; final version received: October 1997
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Related research
Keywords: Transaction costs; super-replicating strategies; viscosity solutions;

Find related papers by JEL classification:
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Michael Monoyios & Alberto Montagnoli, 2002. "Efficient Option Pricing with Transaction Costs," Public Policy Discussion Papers 02-22, Economics and Finance Section, School of Social Sciences, Brunel University. [Downloadable!]
  2. Michael Monoyios & Alberto Montagnoli, 2002. "Efficient Option Pricing with Transaction Costs," Economics and Finance Discussion Papers 02-22, Economics and Finance Section, School of Social Sciences, Brunel University. [Downloadable!]
  3. C. Atkinson & C. A. Alexandropoulos, 2006. "Pricing a European Basket Option in the Presence of Proportional Transaction Costs," Applied Mathematical Finance, Taylor and Francis Journals, vol. 13(3), pages 191-214, September. [Downloadable!] (restricted)
  4. Frank de Jong, 2005. "Valuation of pension liabilities in incomplete markets," DNB Working Papers 067, Netherlands Central Bank, Research Department. [Downloadable!]
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