Skip to main content
Log in

Local time, coupling and the passport option

  • Published:
Finance and Stochastics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Additional information

Manuscript received: August 1998; final version received: December 1998

Rights and permissions

Reprints and permissions

About this article

Cite this article

Henderson, V., Hobson, D. Local time, coupling and the passport option. Finance Stochast 4, 69–80 (2000). https://doi.org/10.1007/s007800050003

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s007800050003

Navigation