Replicating Portfolios for Lookback Options in Discrete Time with Transaction Costs
Date Issued
2005
Date
2005
Author(s)
Huang, Chien-Hao
DOI
en-US
Abstract
We consider the price of the lookback options in the imperfect market where transaction costs are present. The standard Black - Scholes option pricing methodology is no longer valid since the market is imperfect. We prove that there still exists a unique replicating portfolio for the long lookback call option with floating stike in a binomial framework. We follow three articles to prove this result. Boyle and Vorst (1992) derive self-financing strategies perfectly replicating the final payoffs to long positions in European call and put options in a binomial framework assuming proportional transaction costs on trades in the stocks. Next, Palmer (2001) derives some results about replicating portfolios and super-replicating portfolios in the one-period model. Further, Cheuk and Vorst (1997) show that a one-state variable binomial model for lookback options can be constructed with the same computational complexity as the standard binomial model. In this paper, we use these results and new lemmas of our own to
prove that there exists a unique replicating portfolio for a long lookback call option with floating strike in discrete time with proportional transaction costs.
Subjects
選擇權複製
交易成本
回顧式選擇權
離散時間
Option replication
Transaction costs
Lookback options
Discrete time
Type
thesis
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