Quantitative Trading Curriculum

Build the core tools of quantitative finance independently, from price simulation to the backtesting of algorithmic strategies.

Price paths simulated with geometric Brownian motion.

• Simulated prices with geometric Brownian motion (GBM).
• Priced options with Black–Scholes and visualized the Greeks.
• Applied Monte Carlo methods.
• Modeled the volatility surface and extracted implied volatility with the Newton–Raphson method.
• Backtested algorithmic strategies: moving-average crossover, RSI, Bollinger Bands.

A working implementation of each module and a backtesting framework for three technical strategies.

• GBM assumes normally distributed returns and constant volatility: it does not capture fat tails or volatility clustering.
• Backtests on historical data are exposed to overfitting. Without transaction costs and slippage, results are optimistic.
• Newton–Raphson may fail to converge for deep out-of-the-money options, where vega is close to zero.

To validate each module against a known result before building on it: the Monte Carlo price must converge to Black–Scholes, and implied volatility must return the starting price.