Barrier Option Pricing Using Adjusted Transition Probabilities

Posted: 22 Feb 2007

See all articles by Giovanni Barone-Adesi

Giovanni Barone-Adesi

University of Lugano; Swiss Finance Institute

Nicola Fusari

Johns Hopkins University - Carey Business School; Northwestern University - Kellogg School of Management

John Theal

Banque Centrale du Luxembourg

Date Written: February 2007

Abstract

In the existing literature on barrier options, much effort has been exerted to ensure convergence through placing the barrier in close proximity to, or directly onto, the nodes of the tree lattice. In this paper we show that this may not be necessary to achieve accurate option price approximations. Using the Cox/Ross/Rubinstein binomial tree model and a suitable transition probability adjustment we demonstrate that our "probability-adjusted" model exhibits increased convergence to the analytical option price. We study the convergence properties of various types of options including (but not limited to) double knock-out, exponential barrier, double (constant) linear barriers and linear time-varying barriers. For options whose strike price is close to the barrier we are able to obtain numerical results where other models fail and, although convergence tends to be slow, we are able to calculate reasonable approximations to the analytical option price without having to reposition the lattice nodes.

Keywords: barrier option, binomial tree, convergence rate, transition probability

JEL Classification: C63, G12

Suggested Citation

Barone-Adesi, Giovanni and Fusari, Nicola and Theal, John, Barrier Option Pricing Using Adjusted Transition Probabilities (February 2007). https://doi.org/10.3905/JOD.2008.16.2.036; Swiss Finance Institute Research Paper No. 07-02. Available at SSRN: https://ssrn.com/abstract=964623 or http://dx.doi.org/10.2139/ssrn.964623

Giovanni Barone-Adesi (Contact Author)

University of Lugano ( email )

Via Buffi 13
CH-6904 Lugano
Switzerland
+41 58 666 4671 (Phone)
+41 58 666 46 47 (Fax)

Swiss Finance Institute

c/o University of Geneva
40 Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Nicola Fusari

Johns Hopkins University - Carey Business School ( email )

100 International Drive
Baltimore, MD 21202
United States

Northwestern University - Kellogg School of Management ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

John Theal

Banque Centrale du Luxembourg ( email )

2 Boulevard Royal
Luxemburg, L-2983
Luxembourg

Register to save articles to
your library

Register

Paper statistics

Abstract Views
3,828
PlumX Metrics