This paper surveys some of the literature on American option pricing, in particular the representations of McKean (1965), Kim (1990) and Carr, Jarrow and Myneni (1992). It is proposed that the approach regarding the problem as a free boundary value problem, and solving this via incomplete...

This paper considers the Fourier transform approach to derive the implicit integral equation for the price of an American call option in the case where the underlying asset follows a jump-diffusion process. Using the method of Jamshidian (1992), we demonstrate that the call option price is given...

In this paper we derive the implicit integral equation for the price of an American call option in the case where the underlying asset follows a jump-diffusion process. We extend McKean's incomplete Fourier transform approach to solve the free boundary problem under Merton's framework, with the...

This paper presents a numerical method for pricing American call options where the underlying asset price follows a jump-diffusion process. The method is based on the Fourier-Hermite series expansions of Chiarella, El-Hassan & Kucera (1999), which we extend to allow for Poisson jumps, in the...

This paper considers the problem of pricing American options when the dynamics of the underlying are driven both by stochastic volatility following a square root process as used by Heston (1993) and by a Poisson jump process as introduced by Merton (1976). The two-factor homogeneous...

This paper presents a numerical method for pricing American call options where the underlying asset price follows a jump-diffusion process. The method is based on the Fourier-Hermite series expansions of Chiarella, El-Hassan and Kucera (1999), which we extend to allow for Poisson jumps, in the...

This paper considers the problem of pricing American options when the dynamics of the underlying are driven by both stochastic volatility following a square root process as used by Heston (1993), and by a Poisson jump process as introduced by Merton (1976). Probability arguments are invoked to...

This paper provides an extension of McKean’s (1965) incomplete Fourier transform method to solve the two-factor partial differential equation for the price and early exercise surface of an American call option, in the case where the volatility of the underlying evolves randomly. The...