Local time, coupling and the passport option

Vicky Henderson () and David Hobson ()
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Vicky Henderson: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK Manuscript
David Hobson: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK Manuscript

Finance and Stochastics, 2000, vol. 4, issue 1, 69-80

Abstract: A passport option, as introduced and marketed by Bankers Trust, is a call option on the balance of a trading account. The strategy that this account follows is chosen by the option holder, subject to position limits. We derive a simplified form for the price of the passport option using local time. A key insight is that Tanaka's formula and the Skorokhod Lemma allow us to prove a direct relationship between the prices of passport and lookback options. Explicit calculations are provided in the case where the underlying is an exponential Brownian motion. A further issue in the analysis of passport options is the identification of the optimal strategy. The second contribution of this article is to extend existing results on the form of the optimal strategy from the exponential Brownian motion model to a wide class of alternative price processes. We achieve this using coupling arguments.

Keywords: Passport option; local time; coupling; Skorokhod lemma; option pricing (search for similar items in EconPapers)
JEL-codes: G12 G13 (search for similar items in EconPapers)
Date: 1999-10-29
Note: received: August 1998; final version received: December 1998
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