Valuation of American strangle option: Variational inequality approach

Abstract

In this paper, we investigate a parabolic variational inequality problem associated with the American strangle option pricing. We obtain the existence and uniqueness of W 2,1 p,loc solution to the problem. Also, we analyze the smoothness and monotonicity of two free boundaries. Finally, numerical results of the model based on this problem are described and used to show the boundary properties and the price behavior.

On the American style futures contracts

“…Note that the limit above is zero due to Lemma 1. We can easily check that function (14) achieves its maximum namely for c given by formula (11) and it leads to price (12).…”

“…The other class of American derivatives leads to an optimal region consisting of two parts -thus a first exit from a strip arises. Such instruments are the straddle options, [1,9], their extensions named strangles, [6,12,14,15,21,22,32], cancelable American options, also known as Israeli or game options, [8,16,18,24,31,30], etc.…”

American strangle options with arbitrary strikes

“…An approach based on deriving the limits for the boundaries by the use of capping is presented by Ma et al (2018). The variational inequalities method is presented by Jeon and Oh (2019). This method is closely related to the corresponding two‐sided free boundary differential problem which describes the strangle pricing.…”