Perpetual options and Canadization through fluctuation theory

Reference:

Kyprianou, A. E. and Pistorius, M. R., 2003. Perpetual options and Canadization through fluctuation theory. Annals of Applied Probability, 13 (3), pp. 1077-1098.

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Official URL:

http://dx.doi.org/10.1214/aoap/1060202835

Abstract

In this article it is shown that one is able to evaluate the price of perpetual calls, puts, Russian and integral options directly as the Laplace transform of a stopping time of an appropriate diffusion using standard fluctuation theory. This approach is offered in contrast to the approach of optimal stopping through free boundary problems. Following ideas of Carr [Rev. Fin. Studies 11 (1998) 597--626], we discuss the Canadization of these options as a method of approximation to their finite time counterparts. Fluctuation theory is again used in this case.

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