Various Passport Options and Their Valuation

H. Ahn, A. Penaud, P. Wilmott

Abstract

The passport option is a call option on the balance of a trading account. The option holder retains the gain from trading, while the writer is liable for the loss. We establish pricing equations for various passport options including the multi-asset passport and those with discrete trading constraints. The results are typically known as the Hamilton- Jacobi-Bellman equations and multiple layers of free boundary partial dierential equations for a sequence of optimal stopping times. Also we examine the gain by selling passport options to utility maximising investors and to investors who guess the market from imperfect information.

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