Capstone Project: Monte Carlo Methods and their Applications to Finance

Repository for my MA4198 Capstone Project, read in Semester 1, AY2526 at NUS. Supervised by Prof. Ren Weiqing.

Overview

This repository contains the code and documentation for the capstone project on Monte Carlo methods with applications to finance. The project explores Monte Carlo techniques and their applications in financial modeling, risk assessment, and option pricing. Several variance reduction techniques are implemented and compared, such as Importance Sampling and Control Variates.

In addition, an implementation of Kernel Regression for fitting Control Functionals is provided, following the methodology outlined in the paper "Control Functionals for Monte Carlo Integration" by Oates et al. (2017).

Structure

• src/: Contains Jupyter notebooks and Python scripts implementing various reduction techniques. Many exercises and examples in the book "Monte Carlo Simulation with Applications to Finance" by Hui Wang are referenced and implemented here.
• report/: Contains the source files for the project report in markdown and Typst formats.
• resources/: Contains images, rich media, and other files used in the report.

References

• Oates, C. J., Girolami, M., & Chopin, N. (2017). Control Functionals for Monte Carlo Integration. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 79(3), 695-718. Link to Paper