Mathematical analysis of the two-color partial rainbow options

Authors: Chang, Der-Chen¹; Chang, Eric C.²; Fan, Haitao¹; Nhieu, Duy-Minh¹

Source: Applicable Analysis, Volume 84, Number 7, July 2005 , pp. 737-757(21)

Publisher: Taylor and Francis Ltd

Abstract:

In this article, two-color partial rainbow options (TCPROs) are proposed. Such options allow holders to choose between the two underlying vanilla options at a specified time before expiry. Examples of benefits of TCPROs to both holders and issuers are given. Pricing formulae for such options are derived. The extra premium due to the choosing feature of a TCPRO, called the price of choice, is a nonnegative decreasing function of the correlation coefficient of the two underlying assets and the remaining time to choose. Numerical results are obtained to show that while TCPROs are more valuable than the underlying vanilla options, their risk parameters such as delta and gamma are smaller.

Keywords: Pricing; Options; Integral representation; Two-color rainbow; 1991 Mathematics Subject Classifications:; 91B28; 90A12

Document Type: Research article

DOI: http://dx.doi.org/10.1080/00036810500047774

Affiliations: 1: Department of Mathematics, Georgetown University, Washington, DC 20057, USA 2: School of Business, Hong Kong University, Hong Kong

Publication date: 2005-07-01

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