Topics in matrix analysis
Computational frameworks for the fast Fourier transform
Computational frameworks for the fast Fourier transform
A Jump-Diffusion Model for Option Pricing
Management Science
A penalty method for American options with jump diffusion processes
Numerische Mathematik
An iterative method for pricing American options under jump-diffusion models
Applied Numerical Mathematics
SIAM Journal on Financial Mathematics
A Second-Order Tridiagonal Method for American Options under Jump-Diffusion Models
SIAM Journal on Scientific Computing
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 new high-order compact scheme for American options under jump-diffusion processes
International Journal of Business Intelligence and Data Mining
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A jump-diffusion model for a single-asset market is considered. Under this assumption the value of a European contingency claim satisfies a general partial integro-differential equation (PIDE). The equation is localized and discretized in space using finite differences and finite elements and in time by the second order backward differentiation formula (BDF2). The resulting system is solved by an iterative method based on a simple splitting of the matrix. Using the fast Fourier transform, the amount of work per iteration may be reduced to O(nlog"2n) and only O(n) entries need to be stored for each time level. Numerical results showing the quadratic convergence of the methods are given for Merton's model and Kou's model.