Valuation of American Strangles Through an Optimized Lower–Upper Bound Approach

Abstract

In this paper, we construct tight lower and upper bounds for the price of an American strangle, which is a special type of strangle consisting of long positions in an American put and an American call, where the early exercise of one side of the position will knock out the remaining side. This contract was studied in Chiarella and Ziogas (J Econ Dyn Control 29:31–62, 2005) with the corresponding nonlinear integral equations derived, which are hard to be solved efficiently through numerical methods. We extend the approach in the paper of Broadie and Detemple (Rev Finance Stud 9:1211–1250, 1996) from the case of American call options to the case of American strangles. We establish theoretical properties of the lower and upper bounds, and propose a sequential optimization algorithm in approximating the early exercise boundary of the American strangle. The theoretical bounds obtained can be easily evaluated, and numerical examples confirm the accuracy of the approximations compared to the literature.