CLA's, PLA's and a new method for pricing general passport options

Peter Buchen and Hamish Malloch

Quantitative Finance, 2014, vol. 14, issue 7, 1201-1209

Abstract: This paper is primarily concerned with pricing a general passport option (GPO) within the standard Black-Scholes framework. We show that in all possible cases of the allowed trading strategy, the price can be decomposed into simple portfolios of standard European calls and puts and a contract we call a 'PLA' or a put on the log-asset price. For completeness, we also introduce the call on the log-asset price (or CLA) and explore their properties and applications. The decomposition of the GPO into its constituent parts is achieved with the help of the Method of Images to convert certain barrier option payoffs into equivalent European payoffs. This technique considerably simplifies the calculation and adds significant transparency to what is otherwise regarded as very complex problem. Curiously, a spin-off of the method to price the GPO suggests an alternative and simpler way to price lookback options.

Date: 2014
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DOI: 10.1080/14697688.2014.882011

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