Lookback Option Valuation: A Binomial Approach
Date Issued
2006
Date
2006
Author(s)
Hou, Kun-Hong
DOI
en-US
Abstract
Working in the framework of Cox, Ross and Rubinstein (1979), Cheuk and Vorst (1997) derive one-state variable binomial models for lookback options using a change of numeraire. Due to its efficiency, their method has been the most attractive binomial approach to pricing lookback options while the observation frequency is investigated. However, it seems a bit complicated to price discretely sampled options.
Other than Cheuk and Vorst's change of numeraire, there is an alternative to derive the equivalent models. Choi and Jameson (2003) propose a simplified method to develop one-state variable binomial models for European lookback options without considering two important extensions --- the American type and observation frequency. They do not also give a rigorous and clear proof.
In this paper, following Cox et al. (1979) arbitrage arguments, we develop equivalent one-state variable binomial models for lookback options on the basis of the idea of Choi and Jameson (2003): First, we construct the same models for European options as those in Choi and Jameson (2003) and give a more apprehensible proof. Moreover, we extend these models to cope with American and discretely sampled options, and then derive one-state variable binomial models for these variants. Finally we compare our models with others available. Our models perform as well as Cheuk and Vorst's in terms of efficiency, but are much more intuitive and simpler, especially for discretely sampled options. For this reason, the binomial valuation method of this paper are preferred over that of Cheuk and Vorst (1997).
Subjects
單狀態變數
二項模型
回顧選擇權
觀察頻率
One-state variable
Binomial models
Lookback options
Observation frequency
Type
thesis