Quantitative Finance

Financial Markets

Study of how financial markets operate, how assets are traded, and how macroeconomic, institutional and behavioural forces influence prices, liquidity and volatility.

• Market structure across equities, fixed income, commodities, derivatives and digital assets.
• Liquidity, spreads, order books, transaction costs and market efficiency.
• Macroeconomic indicators, monetary policy, yield curves and cross-asset relationships.
• Anomalies, behavioural deviations and empirical limits of market efficiency.

Asset Pricing

Analysis of how financial assets are valued under uncertainty, with emphasis on expected returns, risk premia, factor exposures and stochastic discount factors.

E[R_i] - R_f = β_i (E[R_m] - R_f)

• Capital Asset Pricing Model and empirical limitations.
• Fama-French factor models, momentum and cross-sectional return anomalies.
• Stochastic discount factor interpretation of asset prices.
• Linear factor models and regression-based empirical testing.

Portfolio Theory

Mathematical study of capital allocation under uncertainty, focusing on risk-return trade-offs, diversification, constraints and robust portfolio construction.

minimize:   wᵀΣw
subject to: μᵀw ≥ R_target,   1ᵀw = 1

• Markowitz mean-variance efficiency and the efficient frontier.
• Risk parity, minimum variance and constrained allocation methods.
• Black-Litterman model for incorporating subjective views.
• Robust covariance estimation and shrinkage methods.

Risk Management

Frameworks for measuring, modelling and controlling financial risk across portfolios, strategies and trading systems.

VaR_α(L) = inf { l ∈ R : P(L > l) ≤ 1 - α }

• Value at Risk, Expected Shortfall and drawdown-based measures.
• Stress testing, scenario analysis and tail-risk estimation.
• Volatility targeting, leverage constraints and exposure limits.
• Risk decomposition by asset, factor, sector and strategy component.

Derivatives

Study of derivative instruments and pricing frameworks, with focus on options, futures, arbitrage-free valuation and stochastic processes.

∂V/∂t + 1/2 σ²S² ∂²V/∂S² + rS ∂V/∂S - rV = 0

• Forwards, futures, swaps, vanilla options and option Greeks.
• No-arbitrage pricing, replication arguments and risk-neutral valuation.
• Binomial trees, Black-Scholes, Monte Carlo and finite difference methods.
• Volatility smiles, implied volatility and model calibration.

Backtesting & Strategy

Design and evaluation of systematic trading strategies using historical data, realistic assumptions and robust performance analysis.

• Signal generation, position sizing, transaction costs and portfolio accounting.
• Walk-forward testing, train/test splits and out-of-sample validation.
• Performance metrics including Sharpe ratio, Sortino ratio, max drawdown and turnover.
• Common pitfalls: look-ahead bias, survivorship bias, overfitting and data snooping.

Market Microstructure

Study of how trading mechanisms, order books, liquidity providers and market participants shape price formation at high frequency.

• Limit order books, bid-ask spreads, depth, imbalance and liquidity.
• Price impact, adverse selection and execution costs.
• High-frequency trading, latency, market fragmentation and venue selection.
• Empirical analysis of tick-level and intraday financial data.

Reading Programme

The following reading programme structures the books and references I am studying or plan to study in order to strengthen my foundations in mathematical finance, quantitative research and financial machine learning.

A more complete reading list is available in the Mathematics page under the Books Section .