Volume 13, Issue 4
Improved ADI Parallel Difference Method for Quanto Options Pricing Model

X.-Z. Yang, F. Zhang & L.-F. Wu

DOI:

Int. J. Numer. Anal. Mod., 13 (2016), pp. 569-586

Published online: 2016-07

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  • Abstract

The quanto options pricing model is a typical two-dimensional Black-Scholes equation with a mixed derivative term, and it has been increasingly attracting interest over the last decade. A kind of improved alternating direction implicit methods, which is based on the Douglas-Rachford (D-R ADI) and Craig-Sneyd (C-S ADI) split forms, is given in this paper for solving the quanto options pricing model. The improved ADI methods first split the original problem into two separate one-dimensional problems, and then solve the tri-diagonal matrix equations at each time-step. There are several advantages in this method such as: parallel property, unconditional stability, convergency and better accuracy. The numerical experiments show that this kind of methods is very efficient compared to the existent explicit finite difference method. In addition, because of the natural parallel property of the improved ADI methods, the parallel computing is very easy, and about 50% computational cost can been saved. Thus the improved ADI methods can be used to solve the multi-asset option pricing problems effectively.

  • Keywords

Quanto options pricing model two-dimensional Black-Scholes equation improved ADI method parallel computing numerical experiments

  • AMS Subject Headings

65Y05 91B24

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-569, author = {X.-Z. Yang, F. Zhang and L.-F. Wu}, title = {Improved ADI Parallel Difference Method for Quanto Options Pricing Model}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {4}, pages = {569--586}, abstract = {The quanto options pricing model is a typical two-dimensional Black-Scholes equation with a mixed derivative term, and it has been increasingly attracting interest over the last decade. A kind of improved alternating direction implicit methods, which is based on the Douglas-Rachford (D-R ADI) and Craig-Sneyd (C-S ADI) split forms, is given in this paper for solving the quanto options pricing model. The improved ADI methods first split the original problem into two separate one-dimensional problems, and then solve the tri-diagonal matrix equations at each time-step. There are several advantages in this method such as: parallel property, unconditional stability, convergency and better accuracy. The numerical experiments show that this kind of methods is very efficient compared to the existent explicit finite difference method. In addition, because of the natural parallel property of the improved ADI methods, the parallel computing is very easy, and about 50% computational cost can been saved. Thus the improved ADI methods can be used to solve the multi-asset option pricing problems effectively.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/453.html} }
TY - JOUR T1 - Improved ADI Parallel Difference Method for Quanto Options Pricing Model AU - X.-Z. Yang, F. Zhang & L.-F. Wu JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 569 EP - 586 PY - 2016 DA - 2016/07 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/453.html KW - Quanto options pricing model KW - two-dimensional Black-Scholes equation KW - improved ADI method KW - parallel computing KW - numerical experiments AB - The quanto options pricing model is a typical two-dimensional Black-Scholes equation with a mixed derivative term, and it has been increasingly attracting interest over the last decade. A kind of improved alternating direction implicit methods, which is based on the Douglas-Rachford (D-R ADI) and Craig-Sneyd (C-S ADI) split forms, is given in this paper for solving the quanto options pricing model. The improved ADI methods first split the original problem into two separate one-dimensional problems, and then solve the tri-diagonal matrix equations at each time-step. There are several advantages in this method such as: parallel property, unconditional stability, convergency and better accuracy. The numerical experiments show that this kind of methods is very efficient compared to the existent explicit finite difference method. In addition, because of the natural parallel property of the improved ADI methods, the parallel computing is very easy, and about 50% computational cost can been saved. Thus the improved ADI methods can be used to solve the multi-asset option pricing problems effectively.
X.-Z. Yang, F. Zhang & L.-F. Wu. (1970). Improved ADI Parallel Difference Method for Quanto Options Pricing Model. International Journal of Numerical Analysis and Modeling. 13 (4). 569-586. doi:
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