A modified binomial tree method for currency lookback options
type: Item
instance of: scholarly article
title: A modified binomial tree method for currency lookback options
zbMATH Open document ID: 0994.91021
author: Min Dai
publication date: 2001-02-18T00:00:00Z
review text: Lookback options are path dependent options whose payoffs depend on the maximum or the minimum of the underlying asset price during the life of options. \textit{Cox}, \textit{Ross} and \textit{Rubinstein} [J. Financ. Econ. 7, No. 3, 229--263 (1979; Zbl 1131.91333)] have proposed the `binomial tree method' as a discrete model and it is the most, popular numerical approach to the pricing option. Since lookback options are mostly structured with a foreign exchange as an underlying variable, such options are treated with continuously monitoring. It has also been observed that the binomial tree method for currency lookback options converges very slowly. In this paper the author has developed a more efficient scheme on the basis of PDE approach known as the modified binomial tree method. This method possesses one order of accuracy and its efficiency is demonstrated by numerical experiments. It has been shown that the values of currency lookback options computed from the modified binomial tree method converge to the true solutions of the corresponding continuous model. Due to consistency, the convergence can be directly deduced by the Lax theorem for European cases. But for American currency lookback put options, it causes some difficulties.
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 35Q91
Mathematics Subject Classification ID: 35K85
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 1530090
zbMATH Keywords: path dependent options
zbMATH Keywords: PDE approach
zbMATH Keywords: currency lookback options
zbMATH Keywords: modified binomial tree method
reviewed by: C. L. Parihar
MaRDI profile type: Publication
full work available at URL: s101140000068
OpenAlex ID: W2049215413
cites work: Q4349551
cites work: Q4863379
cites work: Option pricing: A simplified approach
cites work: PRICING OF AMERICAN PATH-DEPENDENT CONTINGENT CLAIMS
cites work: Q4328944
cites work: Q4855462
cites work: User’s guide to viscosity solutions of second order partial differential equations
cites work: Q3355178
DOI: 10.1007/S101140000068
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published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1530090