First Phase: Stationarity and co-integration

• try auto regressive models like AR, MA, ARIMA and GARCH
• factor models like fama french 3 and 5 factor models

Prove why a standard XGBoost model mapping features to price would fail, and why using ‘log returns’ as a target might work better ?

Build a simple linear regressor for a stock’s return, are the residuals white noise ? Why or why not

Second Phase:

• no arbitrage principle
• binomial trees and black scholes
• bond pricing, yield curve and duration in context of fixed income

Implement the black scholes formula in python Then write a root finding algorithm (like newton raphson) to calculate implied volatility from market prices.

Simular a stock price using Geometric Brownian Motion and hedge an option possible.

Third Phase

Derive the SDE for a ‘Lookback Option’

Build a monte carlo engine that handles ‘barrier option’, compare speed and accuracy against a closed form solution.