Abstract
In this paper, a new second-order exponential time differencing (ETD) method based on the Cox and Matthews approach is developed and applied for pricing American options with transaction cost. The method is seen to be strongly stable and highly efficient for solving the nonlinear Black-Scholes model. Furthermore, it does not incur unwanted oscillations unlike the ETD-Crank-Nicolson method for exotic path-dependent American options. The computational efficiency and reliability of the new method are demonstrated by numerical examples and by comparing it with the existing methods.
| Original language | English |
|---|---|
| Pages (from-to) | 1239-1254 |
| Number of pages | 16 |
| Journal | International Journal of Computer Mathematics |
| Volume | 89 |
| Issue number | 9 |
| DOIs | |
| State | Published - 1 Jun 2012 |
Bibliographical note
Funding Information:The work of M. Yousuf was supported by the Fast Track Project # FT100003, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. The third author and consultant of the project A.Q.M. Khaliq thanks KFUPM for the hospitality during his visit. The authors are grateful to the anonymous referees for their constructive comments and valuable suggestions, which have improved the quality of this paper.
Keywords
- butterfly spread
- discrete barrier option
- exponential time differencing
- nonlinear Black-Scholes model
- transaction cost
ASJC Scopus subject areas
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics