The finite element method using MATLAB (2nd ed.)
The finite element method using MATLAB (2nd ed.)
Exponential time differencing for stiff systems
Journal of Computational Physics
A penalty method for American options with jump diffusion processes
Numerische Mathematik
Numerical valuation of options with jumps in the underlying
Applied Numerical Mathematics
Option Pricing Under a Double Exponential Jump Diffusion Model
Management Science
Numerical pricing of options using high-order compact finite difference schemes
Journal of Computational and Applied Mathematics
Exponential time integration and Chebychev discretisation schemes for fast pricing of options
Applied Numerical Mathematics
Comparison of methods for evaluating functions of a matrix exponential
Applied Numerical Mathematics
Pricing Options in Jump-Diffusion Models: An Extrapolation Approach
Operations Research
Using vector divisions in solving the linear complementarity problem
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
| Hi-index | 7.29 |
We consider exponential time integration schemes for fast numerical pricing of European, American, barrier and butterfly options when the stock price follows a dynamics described by a jump-diffusion process. The resulting pricing equation which is in the form of a partial integro-differential equation is approximated in space using finite elements. Our methods require the computation of a single matrix exponential and we demonstrate using a wide range of numerical tests that the combination of exponential integrators and finite element discretisations with quadratic basis functions leads to highly accurate algorithms for cases when the jump magnitude is Gaussian. Comparison with other time-stepping methods are also carried out to illustrate the effectiveness of our methods.