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

18 Pages Posted: 2 Oct 2008

See all articles by Mitya Boyarchenko

Mitya Boyarchenko

University of Michigan - Department of Mathematics

Date Written: September 29, 2008

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.

Keywords: Option pricing, barrier options, double barrier options, Carr's randomization, Canadization, analytic method of lines, Levy processes

JEL Classification: G13

Suggested Citation

Boyarchenko, Mitya, Carr's Randomization for Finite-Lived Barrier Options: Proof of Convergence (September 29, 2008). Available at SSRN: https://ssrn.com/abstract=1275666 or http://dx.doi.org/10.2139/ssrn.1275666

Mitya Boyarchenko (Contact Author)

University of Michigan - Department of Mathematics ( email )

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2074 East Hall
Ann Arbor, MI 48109
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