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Volume 13, Issue 2
High-Order Methods for Exotic Options and Greeks Under Regime-Switching Jump-Diffusion Models

Jingtang Ma, Han Wang, Zhiqiang Zhou & Zhijun Tan

DOI: 10.4208/nmtma.OA-2019-0119

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 497-515.

Published online: 2020-03

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  • 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.

  • Keywords

Option pricing, Greeks, exotic options, Asian options, lookback options, high-order methods.

  • AMS Subject Headings

91G20, 91G60, 91G80

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

mjt@swufe.edu.cn (Jingtang Ma)

117020291003@smail.swufe. edu.cn (Han Wang)

zqzhou hu@yahoo.com (Zhiqiang Zhou)

tzhij@mail.sysu.edu.cn (Zhijun Tan)

  • BibTex
  • RIS
  • TXT
@Article{NMTMA-13-497, author = {Ma , JingtangWang , HanZhou , Zhiqiang and Tan , Zhijun}, 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 = {http://global-sci.org/intro/article_detail/nmtma/15489.html} }
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 -

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.

Ma , JingtangWang , HanZhou , Zhiqiang and Tan , Zhijun. (2020). High-Order Methods for Exotic Options and Greeks Under Regime-Switching Jump-Diffusion Models. Numerical Mathematics: Theory, Methods and Applications. 13 (2). 497-515. doi:10.4208/nmtma.OA-2019-0119
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