@Article{NMTMA-13-2, author = {Zhou, Zhiqiang and Ma, Jingtang and Zhijun, Tan and Wang, Han and Zhou, Zhiqiang and Zhijun, Tan}, title = {High-Order Methods for Exotic Options and Greeks Under Regime-Switching Jump-Diffusion Models}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2020}, volume = {13}, number = {2}, pages = {497--515}, abstract = {

This paper aims to develop high-order numerical methods for solving the system partial differential equations (PDEs) and partial integro-differential equations (PIDEs) arising in exotic option pricing under regime-switching models and regime-switching jump-diffusion models, respectively. Using cubic Hermite polynomials, the high-order collocation methods are proposed to solve the system PDEs and PIDEs. This collocation scheme has the second-order convergence rates in time and fourth-order rates in space. The computation of the Greeks for the options is also studied. Numerical examples are carried out to verify the high-order convergence and show the efficiency for computing the Greeks.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0119}, url = {https://global-sci.com/article/90356/high-order-methods-for-exotic-options-and-greeks-under-regime-switching-jump-diffusion-models} }