Carr's Randomization for Finite-Lived Barrier Options: Proof of Convergence

Abstract

A maturity randomization technique was introduced by Carr (under the name "Canadization") as an efficient method of pricing finite-lived American options (it is equivalent to the "analytic method of lines" used earlier by Carr and Faguet). Since then, Carr's randomization was successfully applied to the valuation of (single and double) barrier options in a number of works. In this article we provide formal justification for the latter methods, by showing that Carr's approximation to the value of a finite-lived barrier option with bounded continuous terminal payoff function always converges to the actual value for a wide class of Levy processes (those of type B or C), including all those that are used in financial modeling.