Pricing of Passport Option

J. Math. Sci. Univ. Tokyo
Vol. 5 (1998), No. 4, Page 747--785.

Nagayama, Izumi
Pricing of Passport Option
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Passport options are derivatives on actively managed funds. There is no known explicit formula for the price of passport options in general. We estimate and analyze the value function, and give the condition that the optimal strategy becomes trivial. We also show an approximation theorem which enables us to compute the value function numerically. Finally we give the explicit formula for the value function in the case that the interest rate is zero by using stochastic analytic approach. This is somehow done in symmetric case by Hyer, Lipton-Lifschitz, and Pugachevsky using partial differential equation approach.

Keywords: passport option, Black \& Scholes model, local time, Skorohod's Theorem, stochastic control

Mathematics Subject Classification (1991): Primary 90A09; Secondary 60J55
Mathematical Reviews Number: MR1675249

Received: 1998-05-21