A proposal for toeplitz matrix calculations
Studies in Applied Mathematics
The spectrum of a family of circulant preconditioned Toeplitz systems
SIAM Journal on Numerical Analysis
Circulant preconditioners for Hermitian Toeplitz systems
SIAM Journal on Matrix Analysis and Applications
The spectra of super-optimal circulant preconditioned Toeplitz systems
SIAM Journal on Numerical Analysis
Optimal and superoptimal circulant preconditioners
SIAM Journal on Matrix Analysis and Applications
Some aspects of circulant preconditioners
SIAM Journal on Scientific Computing
A Jump-Diffusion Model for Option Pricing
Management Science
A penalty method for American options with jump diffusion processes
Numerische Mathematik
Numerical valuation of options with jumps in the underlying
Applied Numerical Mathematics
Fast Numerical Solution of Parabolic Integrodifferential Equations with Applications in Finance
SIAM Journal on Scientific Computing
A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models
SIAM Journal on Numerical Analysis
Iterative Methods for Toeplitz Systems (Numerical Mathematics and Scientific Computation)
Iterative Methods for Toeplitz Systems (Numerical Mathematics and Scientific Computation)
An iterative method for pricing American options under jump-diffusion models
Applied Numerical Mathematics
A new algorithm for solving nearly penta-diagonal Toeplitz linear systems
Computers & Mathematics with Applications
Tri-diagonal preconditioner for pricing options
Journal of Computational and Applied Mathematics
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Jump-diffusion models for the pricing of derivatives lead under certain assumptions to partial integro-differential equations (PIDE). Such a PIDE typically involves a convection term and a non-local integral. We transform the PIDE to eliminate the convection term, discretize it implicitly, and use finite differences on a uniform grid. The resulting dense linear system exhibits so much structure that it can be solved very efficiently by a circulant preconditioned conjugate gradient method. Therefore, this fully implicit scheme requires only on the order of O(nlogn) operations. Second order accuracy is obtained numerically on the whole computational domain for Merton's model.