Optimality of replication in the CRR model with transaction costs

Marek Rutkowski

Applicationes Mathematicae (1998)

  • Volume: 25, Issue: 1, page 29-53
  • ISSN: 1233-7234

Abstract

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Recently, there has been a growing interest in optimization problems associated with the arbitrage pricing of derivative securities in imperfect markets (in particular, in models with transaction costs). In this paper, we examine the valuation and hedging of European claims in the multiplicative binomial model proposed by Cox, Ross and Rubinstein [5] (the CRR model), in the presence of proportional transaction costs. We focus on the optimality of replication; in particular, we provide sufficient conditions for the optimality of the replicating strategy in the case of long and short positions in European options. This work can be seen as a continuation of studies by Bensaid et al. [2] and Edirisinghe et al. [13]. We put, however, more emphasis on the martingale approach to the claims valuation in the presence of transaction costs, focusing on call and put options. The problem of optimality of replication in the CRR model under proportional transaction costs was recently solved in all generality by Stettner[30].

How to cite

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Rutkowski, Marek. "Optimality of replication in the CRR model with transaction costs." Applicationes Mathematicae 25.1 (1998): 29-53. <http://eudml.org/doc/219193>.

@article{Rutkowski1998,
abstract = {Recently, there has been a growing interest in optimization problems associated with the arbitrage pricing of derivative securities in imperfect markets (in particular, in models with transaction costs). In this paper, we examine the valuation and hedging of European claims in the multiplicative binomial model proposed by Cox, Ross and Rubinstein [5] (the CRR model), in the presence of proportional transaction costs. We focus on the optimality of replication; in particular, we provide sufficient conditions for the optimality of the replicating strategy in the case of long and short positions in European options. This work can be seen as a continuation of studies by Bensaid et al. [2] and Edirisinghe et al. [13]. We put, however, more emphasis on the martingale approach to the claims valuation in the presence of transaction costs, focusing on call and put options. The problem of optimality of replication in the CRR model under proportional transaction costs was recently solved in all generality by Stettner[30].},
author = {Rutkowski, Marek},
journal = {Applicationes Mathematicae},
keywords = {transaction costs; martingale measure; super-hedging; option pricing; arbitrage pricing; imperfect markets; European claims; multiplicative binomial model; proportional transaction costs},
language = {eng},
number = {1},
pages = {29-53},
title = {Optimality of replication in the CRR model with transaction costs},
url = {http://eudml.org/doc/219193},
volume = {25},
year = {1998},
}

TY - JOUR
AU - Rutkowski, Marek
TI - Optimality of replication in the CRR model with transaction costs
JO - Applicationes Mathematicae
PY - 1998
VL - 25
IS - 1
SP - 29
EP - 53
AB - Recently, there has been a growing interest in optimization problems associated with the arbitrage pricing of derivative securities in imperfect markets (in particular, in models with transaction costs). In this paper, we examine the valuation and hedging of European claims in the multiplicative binomial model proposed by Cox, Ross and Rubinstein [5] (the CRR model), in the presence of proportional transaction costs. We focus on the optimality of replication; in particular, we provide sufficient conditions for the optimality of the replicating strategy in the case of long and short positions in European options. This work can be seen as a continuation of studies by Bensaid et al. [2] and Edirisinghe et al. [13]. We put, however, more emphasis on the martingale approach to the claims valuation in the presence of transaction costs, focusing on call and put options. The problem of optimality of replication in the CRR model under proportional transaction costs was recently solved in all generality by Stettner[30].
LA - eng
KW - transaction costs; martingale measure; super-hedging; option pricing; arbitrage pricing; imperfect markets; European claims; multiplicative binomial model; proportional transaction costs
UR - http://eudml.org/doc/219193
ER -

References

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