Optimality of the replicating strategy for American options

Marek Kociński

Applicationes Mathematicae (1999)

  • Volume: 26, Issue: 1, page 93-105
  • ISSN: 1233-7234

Abstract

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The aim of this paper is to study the problem of optimality of replicating strategies associated with pricing of American contingent claims in the Cox-Ross-Rubinstein model with proportional transaction costs. We show that a replication of the option is always possible. We give sufficient conditions for the existence of a replicating strategy which is optimal, and also show an example of an optimal replicating strategy that is not optimal in the global sense.

How to cite

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Kociński, Marek. "Optimality of the replicating strategy for American options." Applicationes Mathematicae 26.1 (1999): 93-105. <http://eudml.org/doc/219228>.

@article{Kociński1999,
abstract = {The aim of this paper is to study the problem of optimality of replicating strategies associated with pricing of American contingent claims in the Cox-Ross-Rubinstein model with proportional transaction costs. We show that a replication of the option is always possible. We give sufficient conditions for the existence of a replicating strategy which is optimal, and also show an example of an optimal replicating strategy that is not optimal in the global sense.},
author = {Kociński, Marek},
journal = {Applicationes Mathematicae},
keywords = {Cox-Ross-Rubinstein model; replicating strategy; American option},
language = {eng},
number = {1},
pages = {93-105},
title = {Optimality of the replicating strategy for American options},
url = {http://eudml.org/doc/219228},
volume = {26},
year = {1999},
}

TY - JOUR
AU - Kociński, Marek
TI - Optimality of the replicating strategy for American options
JO - Applicationes Mathematicae
PY - 1999
VL - 26
IS - 1
SP - 93
EP - 105
AB - The aim of this paper is to study the problem of optimality of replicating strategies associated with pricing of American contingent claims in the Cox-Ross-Rubinstein model with proportional transaction costs. We show that a replication of the option is always possible. We give sufficient conditions for the existence of a replicating strategy which is optimal, and also show an example of an optimal replicating strategy that is not optimal in the global sense.
LA - eng
KW - Cox-Ross-Rubinstein model; replicating strategy; American option
UR - http://eudml.org/doc/219228
ER -

References

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  1. [1] J. Cvitanić, H. Pham and N. Touzi, A closed-form solution to the problem of super-replication under transaction costs, Finance Stochastics 3 (1999), 35-54. Zbl0924.90010
  2. [2] S. Levental and A. V. Skorohod, On the possibility of hedging options in the presence of transaction costs, Ann. Appl. Probab. 7 (1997), 410-443. Zbl0883.90018
  3. [3] M. Musiela and M. Rutkowski, Martingale Methods in Financial Modelling, Springer, Berlin, 1997. Zbl0906.60001
  4. [4] M. Rutkowski, Optimality of replication in the CRR model with transaction costs, Appl. Math. (Warsaw) 25 (1998), 29-53. Zbl0914.90026
  5. [5] Ł. Stettner, Option pricing in the CRR model with proportional transaction costs: A cone transformation approach, ibid. 24 (1997), 475-514. Zbl1043.91511

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