Numerical Methods Projects & Homework

Project 1 – Pairs Trading

This project implements a statistical arbitrage strategy using a pairs trading framework, based on simulating the spread between two correlated stocks.

Details in sub folder summary slides.

Project 2 – Credit Value at Risk (Credit VaR)

This project analyzes the credit risk of a portfolio of BBB-rated bonds using two different modeling approaches:
(A) a Multivariate Gaussian model, and
(B) a Gaussian Copula model.

Details in sub folder summary slides.

Homework 1 – Loaded Die Check

Analyzes whether a die is fair using probabilistic modeling.
Topics covered:

1. Probability distributions
2. Expected values
3. Statistical testing

Homework 2 – Simulate Stock Price (Coke & Pepsi)

Simulates independent stock prices under geometric Brownian motion (GBM).
Topics covered:

1. GBM simulation
2. Visualization of price paths

Homework 3 – VaR Methods

1. Historical VaR
2. Parametric (Gaussian) VaR
3. Risk measure interpretation

Homework 4 – Option Pricing

Derivative:

1. KO European Call/Put Option
2. KO American Call/Put Option

Approach:

1. Black Schole
2. Random Walk
3. Trinomial Tree
4. PDE