Quant Finance Course

Lesson 1 • Financial Markets and Instruments

Surveys equities, fixed income, derivatives, and FX markets. Grounds quantitative methods in real-world market structures and conventions.

Lesson 2 • Core Mathematical Tools

Covers calculus, linear algebra, and optimization as applied to finance. Establishes the mathematical backbone for all subsequent quantitative methods.

Lesson 3 • Statistical Inference for Finance

Teaches estimation, hypothesis testing, and regression fundamentals. Connects statistical reasoning to empirical analysis of financial data.

Lesson 4 • Time Value and Discounting

Establishes present value, compounding, and discount factor mechanics. These concepts underpin all pricing and valuation models covered later.

Lesson 1 • Change of Measure Techniques

Introduces Girsanov's theorem and equivalent martingale measures. Provides the theoretical basis for risk-neutral valuation of derivatives.

Lesson 2 • Random Walks and Brownian Motion

Introduces discrete random walks and their continuous-time limit. Establishes Brownian motion as the fundamental building block of asset price models.

Lesson 3 • Martingales and Filtrations

Teaches martingale theory, filtrations, and optional stopping. These concepts are essential for risk-neutral pricing developed in the next chapter.

Lesson 4 • Jump Processes and Levy Models

Extends continuous diffusions to include jumps via Poisson processes. Prepares students for advanced asset models with fat tails and discontinuities.

Lesson 1 • No-Arbitrage Pricing Principles

Establishes replication, no-arbitrage, and the fundamental theorem of asset pricing. These principles justify all derivative valuation methods that follow.

Lesson 2 • Interest Rate Derivatives Pricing

Prices caps, floors, swaptions, and bonds using short-rate and HJM models. Extends Black-Scholes intuition to fixed-income derivative markets.

Lesson 3 • Volatility Modeling

Covers implied volatility, volatility surfaces, and local and stochastic volatility models. Addresses the Black-Scholes smile and skew observed in markets.

Lesson 4 • Exotic and Structured Products

Prices barrier, Asian, lookback, and digital options using analytical and numerical approaches. Demonstrates how path dependency alters valuation strategies.

Lesson 1 • Calibration and Optimization

Fits model parameters to market prices using least-squares and global optimization. Addresses ill-posedness, regularization, and practical calibration workflows.

Lesson 2 • Binomial and Trinomial Trees

Builds recombining trees for equity and interest rate derivatives. Provides intuitive discrete-time approximations to continuous-time models.

Lesson 3 • Finite Difference Methods

Solves the Black-Scholes PDE numerically using explicit, implicit, and Crank-Nicolson schemes. Connects PDE theory to grid-based computational implementation.

Lesson 4 • Monte Carlo Simulation

Teaches path simulation, variance reduction, and convergence analysis. Monte Carlo is the primary tool for pricing path-dependent and high-dimensional products.

Lesson 1 • Mean-Variance Optimization

Derives the efficient frontier and optimal portfolio weights using Markowitz theory. Establishes the quantitative framework for all portfolio construction methods.

Lesson 2 • Risk Parity and Alternative Weighting

Introduces equal risk contribution, inverse volatility, and maximum diversification strategies. Provides alternatives to return-forecast-dependent optimization.

Lesson 3 • Robust and Black-Litterman Allocation

Addresses estimation error in mean-variance via robust optimization and Bayesian views. Produces more stable portfolios than classical Markowitz methods.

Lesson 4 • Factor Models and Risk Decomposition

Covers CAPM, multi-factor models, and principal component analysis for returns. Decomposes portfolio risk into systematic and idiosyncratic components.

Lesson 1 • Value at Risk and Expected Shortfall

Derives VaR and CVaR under historical, parametric, and Monte Carlo methods. These are the primary regulatory and internal risk metrics used in practice.

Lesson 2 • Stress Testing and Scenario Analysis

Designs historical and hypothetical stress scenarios to assess tail risk. Complements VaR by capturing risks beyond normal distributional assumptions.

Lesson 3 • Credit Risk Modeling

Covers default probability, loss given default, and credit portfolio models. Provides tools for pricing credit derivatives and managing counterparty exposure.

Lesson 4 • Greeks and Sensitivity Analysis

Measures portfolio sensitivity to market factors using delta, gamma, vega, and DV01. Links derivative Greeks to practical hedging and risk reporting.

Lesson 1 • Statistical Arbitrage and Pairs Trading

Applies cointegration, spread modeling, and entry-exit rules to equity pairs. Demonstrates a complete mean-reversion strategy from signal to execution.

Lesson 2 • Signal Generation and Alpha Research

Identifies and constructs predictive signals from price, fundamental, and alternative data. Establishes the alpha research process that drives systematic strategies.

Lesson 3 • Performance Attribution and Evaluation

Decomposes strategy returns into factor exposures, alpha, and risk contributions. Provides the analytical tools to evaluate and improve live strategies.

Lesson 4 • Execution and Market Impact

Models order execution, slippage, and market impact using empirical frameworks. Bridges strategy design and live trading by quantifying implementation costs.

Lesson 1 • Systemic Risk and Macro Quant Models

Quantifies systemic risk, contagion, and macro factor dynamics using network and time-series models. Prepares students for firm-wide and macro-level risk analysis.

Lesson 2 • XVA and Regulatory Capital

Integrates CVA, FVA, KVA, and MVA into a unified valuation adjustment framework. Addresses capital efficiency and regulatory requirements for derivatives desks.

Lesson 3 • High-Frequency and Microstructure Models

Analyzes order book dynamics, adverse selection, and HFT strategies using microstructure theory. Connects market microstructure to quantitative trading at high frequency.

Lesson 4 • Model Validation and Governance

Establishes model risk management frameworks, validation standards, and documentation practices. Ensures models meet regulatory and internal governance requirements.