Mathematical Finance & Stochastic Processes

Project Description

The goal of this project was to familiarize the students with the basics of mathematical finance - a field of applied mathematics concerned with the modelling of financial markets. The field of mathematical finance is broadly categorised into two branches :-

1) Risk & Portfolio Management
2) Derivatives Pricing Theory

The goal of the project is to equip the students with the basics of both of these branches and build a foundation for further study in this area. Some students who were already familiar with the introductory topics and had some experience with Deep Learning algorithms also pursued a side-project under Shaurya where they developed deep learning models to outperform the Black-Scholes model in a real setting. The details of this project can also be found in the GitHub link mentioned under ‘Resources’

Pre-requisites: None

Mentors

• Aditya Prakash Singh
• Shaurya Jain

Learning Roadmap

1) Basics - In the first part of the project, the student will learn the basics of statistics and coding with Python which are requisite for learning the further topics in the project.
2) Risk & Portfolio Management - The students studied the foundational works of Markowitz and Sharpe here and learnt how to plot the Markowitz efficient frontier for a portfolio of stocks given their historical returns.
3) Derivatives Pricing Theory - In the final part of the project, the students learnt about Stochastic processes (particularly Markov chains) and studied how these can be used to model European-style options using the Black-Scholes formula.

Resources

All the learning resources can be found at the following GitHub link.