Solving American Option Pricing Models by the Front Fixing Method: Numerical Analysis and Computing

Abstract

This paper presents an explicit finite-difference method for nonlinear partial differential equation appearing as a transformed Black-Scholes equation for American put option under logarithmic front fixing transformation. Numerical analysis of the method is provided. The method preserves positivity and monotonicity of the numerical solution. Consistency and stability properties of the scheme are studied. Explicit calculations avoid iterative algorithms for solving nonlinear systems. Theoretical results are confirmed by numerical experiments. Comparison with other approaches shows that the proposed method is accurate and competitive.

A new efficient numerical method for solving American option under regime switching model

“…Fixed domain transformation techniques inspired in Landau ideas [25] have 60 been used by several authors ( [32], [30], [27], [10]) for partial differential equations modelling American option pricing problems. To our knowledge this transformation technique has not been applied before for a partial differential system with several unknown free boundaries, one for each equation.…”

“…Based on the transformation used by the authors in [32], [10] for the case of 65 just one equation, let us consider the multivariable transformation…”

“…This drawback has been overcome with stochastic volatility, jump diffusion and regime 10 switching models.…”

“…In fact, since Landau's ideas [25] the socalled front-fixing method has been used in many fields [13] and by [1,10,11,24,30] for American option problems without switching.…”

“…Firstly, in section 2 by extending the ideas developed in [10], the PDE 45 system (3) is transformed into a new PDE system on a fixed domain where the free boundaries S…”