Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2018; 33(1): 345-360

Online first article September 11, 2017      Printed January 31, 2018

https://doi.org/10.4134/CKMS.c170060

Copyright © The Korean Mathematical Society.

Discount barrier option pricing with a stochastic interest rate: Mellin transform techniques and method of images

Junkee Jeon, Ji-Hun Yoon

Seoul National University, Pusan National University

Abstract

${}$ In finance, barrier options are options contracts with a payoff that depends on whether the price of the underlying asset hits a predetermined barrier level during the option's lifetime. Based on exotic options and random fluctuations of interest rates in the marketplace, we consider discount barrier options with a stochastic interest rate driven by the Hull-White process. This paper derives the closed-form solutions of the discount barrier option and the discount double barrier option using Mellin transform methods and the PDE (partial differential equation) method of images.

Keywords: discount barrier options, discount double barrier options, Mellin transform, method of images

MSC numbers: 60H30