Journal of Applied Mathematics and Decision Sciences
Volume 6 (2002), Issue 1, Pages 51-70

Hedging entry and exit decisions: activating and deactivating barrier options

Laurent Gauthier

15 W 73rd St, Apt 2, New York, NY 10023, USA

Copyright © 2002 Laurent Gauthier. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Abstract. Investment projects and businesses can be entered or exited at a cost, and the theory of real option teaches us how to find optimal activity levels that should trigger entry or exit. However, in practice, different managers or owners operate under different constraints and might apply different thresholds to the same business. We are interested in the hedging of the risk related to the cost of sub-optimal entry or exit. We introduce a new class of derivative products that can hedge this risk. The pricing of these derivatives involves the joint law of a Brownian excursion and its supremum, which is calculated thanks to Bessel processes-related distribution laws.