Barrier Option Pricing by Branching Processes

International Journal of Theoretical and Applied Finance, Vol. 12, No. 7, pp. 1055-1073, 2009

Posted: 21 Apr 2010

See all articles by Georgi K. Mitov

Georgi K. Mitov

Bulgarian Academy of Science

Svetlozar Rachev

Texas Tech University

Young Shin Kim

University of Karlsruhe

Frank J. Fabozzi

EDHEC Business School

Date Written: November 2009

Abstract

This paper examines the pricing of barrier options when the price of the underlying asset is modeled by a branching process in a random environment (BPRE). We derive an analytical formula for the price of an up-and-out call option, one form of a barrier option. Calibration of the model parameters is performed using market prices of standard call options. Our results show that the prices of barrier options that are priced with the BPRE model deviate significantly from those modeled assuming a lognormal process, despite the fact that for standard options, the corresponding differences between the two models are relatively small.

Keywords: Barrier option, up-and-out call option, Bienayme-Galton-Watson branching process, branching process in a random environment

Suggested Citation

Mitov, Georgi K. and Rachev, Svetlozar and Kim, Young Shin and Fabozzi, Frank J., Barrier Option Pricing by Branching Processes (November 2009). International Journal of Theoretical and Applied Finance, Vol. 12, No. 7, pp. 1055-1073, 2009, Available at SSRN: https://ssrn.com/abstract=1515578

Georgi K. Mitov

Bulgarian Academy of Science ( email )

1, 15 Noemvri Str.
1040 Sofia, 1113
United States

Svetlozar Rachev (Contact Author)

Texas Tech University ( email )

Dept of Mathematics and Statistics
Lubbock, TX 79409
United States
631-662-6516 (Phone)

Young Shin Kim

University of Karlsruhe ( email )

Postbox
76128 Karlsruhe, DE 76128
Germany

Frank J. Fabozzi

EDHEC Business School ( email )

France
215 598-8924 (Phone)

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