Search results for "Operator splitting"

Operator splitting methods for American option pricing

2004

Abstract We propose operator splitting methods for solving the linear complementarity problems arising from the pricing of American options. The space discretization of the underlying Black-Scholes Scholes equation is done using a central finite-difference scheme. The time discretization as well as the operator splittings are based on the Crank-Nicolson method and the two-step backward differentiation formula. Numerical experiments show that the operator splitting methodology is much more efficient than the projected SOR, while the accuracy of both methods are similar.

An Operator Splitting Method for Pricing American Options

2008

Pricing American options using partial (integro-)differential equation based methods leads to linear complementarity problems (LCPs). The numerical solution of these problems resulting from the Black-Scholes model, Kou’s jump-diffusion model, and Heston’s stochastic volatility model are considered. The finite difference discretization is described. The solutions of the discrete LCPs are approximated using an operator splitting method which separates the linear problem and the early exercise constraint to two fractional steps. The numerical experiments demonstrate that the prices of options can be computed in a few milliseconds on a PC.

ADI schemes for valuing European options under the Bates model

2018

Abstract This paper is concerned with the adaptation of alternating direction implicit (ADI) time discretization schemes for the numerical solution of partial integro-differential equations (PIDEs) with application to the Bates model in finance. Three different adaptations are formulated and their (von Neumann) stability is analyzed. Ample numerical experiments are provided for the Bates PIDE, illustrating the actual stability and convergence behaviour of the three adaptations.

Application of Operator Splitting Methods in Finance

2016

Financial derivatives pricing aims to find the fair value of a financial contract on an underlying asset. Here we consider option pricing in the partial differential equations framework. The contemporary models lead to one-dimensional or multidimensional parabolic problems of the convection-diffusion type and generalizations thereof. An overview of various operator splitting methods is presented for the efficient numerical solution of these problems.

A Douglas–Rachford method for sparse extreme learning machine

2019

ADI schemes for valuing European options under the Bates model

2018

This paper is concerned with the adaptation of alternating direction implicit (ADI) time discretization schemes for the numerical solution of partial integro-differential equations (PIDEs) with application to the Bates model in finance. Three different adaptations are formulated and their (von Neumann) stability is analyzed. Ample numerical experiments are provided for the Bates PIDE, illustrating the actual stability and convergence behaviour of the three adaptations. peerReviewed