Exponential time integration and Chebychev discretisation schemes for fast pricing of options

Authors:
D. Y. Tangman;A. Gopaul;M. Bhuruth
Affiliations:
Department of Mathematics, University of Mauritius, Reduit, Mauritius;Department of Mathematics, University of Mauritius, Reduit, Mauritius;Department of Mathematics, University of Mauritius, Reduit, Mauritius
Venue:
Applied Numerical Mathematics
Year:
2008

Citing 7
Cited 4

On Krylov Subspace Approximations to the Matrix Exponential Operator

SIAM Journal on Numerical Analysis
Spectral methods in MatLab

Spectral methods in MatLab
A penalty method for American options with jump diffusion processes

Numerische Mathematik
Convergence of numerical schemes for viscosity solutions to integro-differential degenerate parabolic problems arising in financial theory

Numerische Mathematik
Numerical valuation of options with jumps in the underlying

Applied Numerical Mathematics
A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models

SIAM Journal on Numerical Analysis
Numerical pricing of options using high-order compact finite difference schemes

Journal of Computational and Applied Mathematics

Exponential time integration for fast finite element solutions of some financial engineering problems

Journal of Computational and Applied Mathematics
Shift-Invert Arnoldi Approximation to the Toeplitz Matrix Exponential

SIAM Journal on Scientific Computing
Efficient and high accuracy pricing of barrier options under the CEV diffusion

Journal of Computational and Applied Mathematics
A new high-order compact scheme for American options under jump-diffusion processes

International Journal of Business Intelligence and Data Mining

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider exponential time differencing (ETD) schemes for the numerical pricing of options. Special treatments for the implementation of the boundary conditions that arise in finance are described. We show that only one explicit time step computation gives unconditional second order accuracy for European, Barrier and Butterfly spread options under both Black-Scholes geometric Brownian motion model and Merton's jump diffusion model with constant coefficients. In comparison, the commonly used Crank-Nicolson scheme is shown to be only conditionally stable due to lack of L"0-stability. Finally, we describe how the use of spectral spatial discretisation based on a Chebychev grid point concentration strategy gives fourth order accurate option prices for both the Black-Scholes and Merton's jump-diffusion model.