Pricing American currency options in an exponential Lévy model

Abstract

In this article the problem of the American option valuation in a Lévy process setting is analysed. The perpetual case is first considered. Without possible discontinuities (i.e. with negative jumps in the call case), known results concerning the currency option value as well as the exercise boundary are obtained with a martingale approach. With possible discontinuities of the underlying process at the exercise boundary (i.e. with positive jumps in the call case), original results are derived by relying on first passage time and overshoot associated with a Lévy process. For finite life American currency calls, the formula derived by Bates or Zhang, in the context of a negative jump size, is tested. It is basically an extension of the one developed by Mac Millan and extended by Barone-Adesi and Whaley. It is shown that Bates' model generates pretty good results only when the process is continuous at the exercise boundary.

Optimal hitting time and perpetual option in a non-Lévy model: application to real options

“…Note that the approach defined by the framework we consider differs from those of the models in the literature related to both real options and American options. On the contrary to most of the existing literature (see for instance Gerber and Shiu (1998), Mordecki (2002), or Chesney and Jeanblanc (2004)), the underlying process S cannot be written in terms of a Lévy process X t as S 0 exp(X t ). Quite recently, Muroi (2002) considered a general framework involving a possible default for the underlying process of an American option.…”

Mitigating global warming: a real options approach

“…In order to do so, he has to find the supremum, over L and k, of a function f (·, ·). Because the horizon can be considered infinite, it is known in the options literature that the optimal trigger level L * is constant (Merton, 1973;Carr et al, 1992;Chesney and Jeanblanc, 2004).…”

Una fórmula alternativa de valuar opciones americanas

“…donde G(•) es una función que depende de los n factores macroeconómicos, X, y del tiempo, t, α es una constante y dW representa al movimiento browniano, el cual corresponde a la parte estocástica del proceso. 6 . Ahora supongamos que el activo subyacente, S, el cual puede ser representado por un proceso log-normal, en general sigue el proceso o la ecuación diferencial estocástica:…”