Hedging with a correlated asset: Solution of a nonlinear pricing PDE
Journal of Computational and Applied Mathematics
Approximation of jump diffusions in finance and economics
Computational Economics
Numerical solution of two asset jump diffusion models for option valuation
Applied Numerical Mathematics
Exponential time integration and Chebychev discretisation schemes for fast pricing of options
Applied Numerical Mathematics
Efficient solution of a partial integro-differential equation in finance
Applied Numerical Mathematics
Computers & Mathematics with Applications
Difference-Quadrature Schemes for Nonlinear Degenerate Parabolic Integro-PDE
SIAM Journal on Numerical Analysis
SIAM Journal on Financial Mathematics
Tri-diagonal preconditioner for pricing options
Journal of Computational and Applied Mathematics
A Second-order Finite Difference Method for Option Pricing Under Jump-diffusion Models
SIAM Journal on Numerical Analysis
A Reduced Basis for Option Pricing
SIAM Journal on Financial Mathematics
SIAM Journal on Financial Mathematics
Journal of Computational and Applied Mathematics
A Spectral Element Framework for Option Pricing Under General Exponential Lévy Processes
Journal of Scientific Computing
Fast and efficient numerical methods for an extended Black-Scholes model
Computers & Mathematics with Applications
Journal of Scientific Computing
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We present a finite difference method for solving parabolic partial integro-differential equations with possibly singular kernels which arise in option pricing theory when the random evolution of the underlying asset is driven by a Lévy process or, more generally, a time-inhomogeneous jump-diffusion process. We discuss localization to a finite domain and provide an estimate for the localization error under an integrability condition on the Lévy measure. We propose an explicit-implicit finite difference scheme which can be used to price European and barrier options in such models. We study stability and convergence of the scheme proposed and, under additional conditions, provide estimates on the rate of convergence. Numerical tests are performed with smooth and nonsmooth initial conditions.