TY - JOUR
T1 - High-Order Methods for Exotic Options and Greeks Under Regime-Switching Jump-Diffusion Models
AU - Ma , Jingtang
AU - Wang , Han
AU - Zhou , Zhiqiang
AU - Tan , Zhijun
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 497
EP - 515
PY - 2020
DA - 2020/03
SN - 13
DO - http://doi.org/10.4208/nmtma.OA-2019-0119
UR - https://global-sci.org/intro/article_detail/nmtma/15489.html
KW - Option pricing, Greeks, exotic options, Asian options, lookback options, high-order methods.
AB - <p style="text-align: justify;">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.</p>