Abstract
In this paper, we suggest a jump diffusion model in markets during financial crisis. Using risk-neutral pricing, we derive a partial differential equation (P.D.E.) for the prices of European options. We find a closed form solution of the P.D.E. in the particular case where the stock price is too large. Then, we use such a solution as a boundary condition in the numerical treatment of the P.D.E. for any range of stock price. The numerical method adopted is the unconditionally stable Crank-Nicolson method. Illustrative examples are presented.
Original language | English |
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Pages (from-to) | 2319-2326 |
Number of pages | 8 |
Journal | Applied Mathematics and Information Sciences |
Volume | 7 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2013 |
Keywords
- European options
- Financial crisis
- Finite differences method
- Incomplete markets
- Jump-diffusion models
- Series solutions
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics