On Perpetual American Strangles

Abstract

This article analyzes perpetual American strangles with no recourse to advanced numerical techniques. Our analytical approach rests on an analogy with asymmetric rebates of double knock-out barrier options. The optimal exercise policy is modeled by a couple of boundaries that simultaneously solve a system of two nonlinear equations. Numerical investigations then highlight salient features of American strangles and compare them with portfolios of options that may be used as proxies. Overall, results show that these latter are significantly upward biased in terms of prices and that, more dramatically, they lead the holder to exercise inappropriately.