Evaluation of American option prices in a path integral framework using Fourier–Hermite series expansions

The Implied Risk Neutral Density Dynamics: Evidence from the S&P TSX 60 Index

“…Madan and Milne [15] and Abken et al [16] obtained the risk neutral density from Hermite polynomial approximation. Chiarell [17] used the work of Fourier-Hermite to assess the EU and US share options. Bahra [18] and Sherrick et al [19] introduced a nonparametric method to evaluate European options.…”

Hedging using simulation: a least squares approach

“…The numerical technique we use is fully consistent with continuous time stochastic evolution of prices, in fact it is an application of Malliavin (1997) stochastic calculus of variations in the formulation of Bermin (2002), while at a computational level it integrates the 'spectral' point of view proposed in Madan and Milne (1994), Chiarella et al (1999) with the regression approach to the computation of conditional expectations introduced in Carriere (1996).…”

Path Dependent Option Pricing: The Path Integral Partial Averaging Method

“…Chiarella and El-Hassan have applied the method of Eydeland to the pricing of American bond options in the Heath-Jarrow-Morton framework [24]. More recently, Chiarella et-al have devised a deterministic path integral algorithm based on Fourier-Hermite series expansions and applied it to the pricing of American options and point barrier options [25,26]. They report computational times that are a significant improvement over the standard binomial and finite difference methods.…”