Laplace transforms and the American straddle

Abstract

We address the pricing of American straddle options. We use partial Laplace transform techniques due to Evans et al. (1950) to derive a pair of integral equations giving the locations of the optimal exercise boundaries for an American straddle option with a constant dividend yield.

Integral Equation Formulation for Shout options

“…Applying formula (2.4) to a shout call where it is optimal to hold if S < S (1) f (τ), and exercise if S ≥ S (1) f (τ), we find the value of a one-shout call:…”

A note on the perpetual American straddle

“…In this paper we consider the perpetual American straddle: a classical portfolio consisting of a put option and a call option on the same underlying asset with the same strike price. The pricing of the perpetual American straddle has been studied using different approaches and tools: in [1] by applying the theory of Laplace transforms, in [5] by transforming the problem to a "generalized parking problem", in [6] by exploiting "an analogy with asymmetric rebates of double knock-out barrier options", in [7] "by means of the Esscher transform and the optional sampling theorem", and, more recently, by using a combination of several optimization techniques [3] and [4]. The characterizations obtained in these papers are often cumbersome: indeed, in all of these papers the value function and the optimal exercise time are characterized by a solution of a non-linear system of equations consisting of (at least) two equations.…”

Pricing and hedging American and hybrid strangles with finite maturity

“…Past studies on the pricing of American strangles with finite maturity advocated the use of various advanced numerical techniques. Alobaidi & Mallier (2002) used Laplace transforms and derived analytical formulas for pricing American straddles as well as integral equations to locate early exercise boundaries. Unfortunately, the expressions they provide cannot be inverted analytically and they give no recommendation for numerical inversion.…”