Evaluation of American strangles

This paper presents a generalisation of McKean's free boundary value problem for American options by considering an American strangle position, where exercising one side of the payoff early knocks-out the remaining side. The Fourier transform technique is used to derive a coupled integral equation system for the strangle's free boundaries. A numerical algorithm is provided to solve this system, and these free boundaries are then used to determine the price of the American strangle position. Numerical comparisons between the strangle price and the price of a portfolio formed using a long American call and a long American put option are presented.