This project is devoted to methods for simulating paths of stochastic processes that arise in financial mathematics. It first shows three approaches of simulating paths of Brownian and geometric Brownian motions in one dimensional case - random walk, Brownian bridge and principal components constructions. Then there are examples of the application of geometric Brownian motion in option pricing - Asian option and lookback option. In the end, it talks about a simple model of processes with jumps - the jump-diffusion model and two methods of simulating this model. Programs and graphs are showed and all the algorithms are implemented by Matlab.
- Report.pdf: Full report of this project
- scr: Source code for reproducing all the results in the report.
All content in this repository is openly licensed with a CC BY 4.0, which means you're free to use the materials and remix them so long as you credit the source.
If you were to use content from this repo in your own work, please attribute me with a sentence like:
The material is (partially) derived from Zhangdaihong Liu's project "Simulating Sample Paths of Stochastic Processes Arising in Financial Engineering".