Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(5): 1497-1530

Online first article August 25, 2016      Printed September 30, 2016

https://doi.org/10.4134/BKMS.b150789

Copyright © The Korean Mathematical Society.

Pricing external-chained barrier options with exponential barriers

Junkee Jeon and Ji-Hun Yoon

Seoul National University, Pusan National University

Abstract

External barrier options are two-asset options with stochastic variables where the payoff depends on one underlying asset and the barrier depends on another state variable. The barrier state variable determines whether the option is knocked in or out when the value of the variable is above or below some prescribed barrier level. This paper derives the explicit analytic solution of the chained option with an external single or double barrier by utilizing the probabilistic methods - the reflection principle and the change of measure. Before we do this, we examine the closed-form solution of the external barrier option with a single or double-curved barrier using the methods of image and double Mellin transforms. The exact solution of the external barrier option price enables us to obtain the pricing formula of the chained option with the external barrier more easily.

Keywords: chained option, external barriers, double barrier, reflection principle, double Mellin transform

MSC numbers: 60H30

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