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1998-1999 | 25 | 1 | 29-53
Tytuł artykułu

Optimality of replication in the CRR model with transaction costs

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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].
Rocznik
Tom
25
Numer
1
Strony
29-53
Opis fizyczny
Daty
wydano
1998
otrzymano
1996-07-25
poprawiono
1997-01-04
Twórcy
  • Institute of Mathematics, Technical University of Warsaw, 00-661 Warszawa, Poland
Bibliografia
  • [1] M. Avallaneda and A. Parás, Dynamic hedging portfolios for derivative securi- ties in the presence of large transaction costs, Appl. Math. Finance 1 (1994), 165-194.
  • [2] B. Bensaid, J.-P. Lesne, H. Pagès and J. Scheinkman, Derivative asset pricing with transaction costs, Math. Finance 2 (1992), 63-68.
  • [3] P. Boyle and T. Vorst, Option replication in discrete time with transaction costs, J. Finance 47 (1992), 271-293.
  • [4] M. Broadie, J. Cvitanić and M. Soner, Optimal replication of contingent claims under portfolio constraints, preprint, Columbia Univ., 1996.
  • [5] J. C. Cox, S. A. Ross and M. Rubinstein, Option pricing: A simplified approach, J. Financial Economics 7 (1979), 229-263.
  • [6] J. Cvitanić and I. Karatzas, Hedging and portfolio optimization under transaction costs: a martingale approach, Math. Finance 6 (1996), 133-165.
  • [7] M. H. A. Davis, Local time on the stock exchange, in: Stochastic Calculus in Application, J. R. Norris (ed.), Pitman Res. Notes Math. Ser. 197, Longman, London, 1988, 4-28.
  • [8] M. H. A. Davis and J. M. C. Clark, A note on super-replicating strategies, Philos. Trans. Roy. Soc. London Ser. A 347 (1994), 485-494.
  • [9] M. H. A. Davis and A. R. Norman, Portfolio selection with transaction costs, Math. Oper. Res. 15 (1990), 676-713.
  • [10] M. H. A. Davis and V. P. Panas, The writing price of a European contingent claim under proportional transaction costs, Comput. Appl. Math. 13 (1994), 115-157.
  • [11] M. H. A. Davis, V. P. Panas and T. Zariphopoulou, European option pricing with transaction costs, SIAM J. Control Optim. 31 (1993), 470-493.
  • [12] J. C. Dermody and R. T. Rockafellar, Cash stream valuation in the face of transaction costs and taxes, Math. Finance 1 (1991), 31-54.
  • [13] C. Edirisinghe, V. Naik and R. Uppal, Optimal replication of options with transaction costs and trading restrictions, J. Finance Quant. Anal. 28 (1993), 117-138.
  • [14] S. Figlewski, Options arbitrage in imperfect markets, J. Finance 44 (1989), 1289-1311.
  • [15] J. E. Gilster and W. Lee, The effects of transaction costs and different borrowing and lending rates on the option pricing model: a note, ibid. 39 (1984), 1215-1221.
  • [16] J. P. Gould and D. Galai, Transaction costs and the relationship between put and call prices, J. Financial Economics 1 (1974), 105-130.
  • [17] E. R. Grannan and G. H. Swindle, Minimizing transaction costs of option hedging strategies, Math. Finance 6 (1996), 341-364.
  • [18] S. Hodges and A. Neuberger, Optimal replication of contingent claims under transaction costs, Rev. Futures Markets 8 (1989), 222-239.
  • [19] E. Jouini and H. Kallal, Martingales and arbitrage in securities markets with transaction costs, J. Econom. Theory 66 (1995), 178-197.
  • [20] Yu. M. Kabanov and M. Safarian, On Leland's strategy of option pricing with transaction costs, Finance Stochast. 1 (1997), 239-250.
  • [21] S. Kusuoka, Limit theorem on option replication cost with transaction costs, Ann. Appl. Probab. 5 (1995), 198-221.
  • [22] H. E. Leland, Option pricing and replication with transaction costs, J. Finance 40 (1985), 1283-1301.
  • [23] M. J. P. Magill and G. M. Constantinides, Portfolio selection with transactions costs, J. Econom. Theory 13 (1976), 245-263.
  • [24] F. Mercurio and T. Vorst, Option pricing and hedging in discrete time with transaction costs and incomplete markets, in: Mathematics of Derivative Securities, M. Dempster and S. Pliska (eds.), Cambridge Univ. Press, Cambridge, 1996, to appear.
  • [25] Q. Shen, Bid-ask prices for call options with transaction costs, preprint, Univ. of Pennsylvania, 1990.
  • [26] H. Shirakawa and H. Konno, Pricing of options under the proportional transaction costs, preprint, Tokyo Inst. of Technology, 1995.
  • [27] S. E. Shreve and H. M. Soner, Optimal investment and consumption with transaction costs, Ann. Appl. Probab. 4 (1994), 609-692.
  • [28] S. E. Shreve, H. M. Soner and G.-L. Xu, Optimal investment and consumption with two bonds and transaction costs, Math. Finance 1 (1991), 53-84.
  • [29] H. M. Soner, S. E. Shreve and J. Cvitanić, There is no nontrivial hedging portfolio for option pricing with transaction costs, Ann. Appl. Probab. 5 (1995), 327-355.
  • [30] Ł. Stettner, Option pricing in the CRR model with proportional transaction costs: a cone transformation approach, Appl. Math. (Warsaw) 24 (1997), 475-514.
  • [31] S. Swidler and J. D. Diltz, Implied volatilities and transaction costs, J. Finance Quant. Anal. 27 (1992), 437-447.
  • [32] M. Taksar, M. J. Klass and D. Assaf, A diffusion model for optimal portfolio selection in the presence of brokerage fees, Math. Oper. Res. 13 (1988), 277-294.
  • [33] A. Tourin and T. Zariphopoulou, Portfolio selection with transaction costs, in: Seminar on Stochastic Analysis, Random Fields and Applications, Progr. Probab. 36, E. Bolthausen et al. (eds.), Birkhäuser, 1995, 385-391.
  • [34] E. Whalley and P. Wilmott, A hedging strategy and option valuation model with transaction costs, preprint, Oxford Univ., 1992.
  • [35] E. Whalley and P. Wilmott, Derivative pricing and transaction costs, preprint, Oxford Univ., 1992.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv25i1p29bwm
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