A Jump-Diffusion Model for Option Pricing
Management Science
A penalty method for American options with jump diffusion processes
Numerische Mathematik
Numerical Valuation of European and American Options under Kou's Jump-Diffusion Model
SIAM Journal on Scientific Computing
Numerical valuation of options with jumps in the underlying
Applied Numerical Mathematics
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
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We propose an implicit numerical method for pricing American options where the underlying asset follows a jump-diffusion model. Using the fact that the prices of American options are given by linear complementarity problems (LCPs), we combine an implicit finite difference method with an operator splitting method. The proposed method is constructed on three time levels, and the operator splitting method is used to treat American constraints. We concentrate on the formulation of the numerical method which leads to linear systems with tridiagonal coefficient matrices. Numerical experiments show that the implicit method has the second-order convergence rate, and the prices of American options can be obtained in a fraction of a second on a computer.