Perpetual Options and Canadization Through Fluctuation Theory

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 diusion using standard uctuation theory. This approach is oered in contrast to the approach of optimal stopping through free boundary problems [see volume 39,1 of Theory of Probability and its Applications]. Following ideas in [5], we discuss the Canadization of these options as a method of approximation to their nite time counterparts. Fluctuation theory is again used in this case.