Quantitative Finance Course

Lesson 1 • Statistical Inference and Data Analysis

Covers estimation, hypothesis testing, and regression fundamentals. Equips students to extract signals from financial time series.

Lesson 2 • Financial Markets and Instruments Overview

Introduces asset classes, market structure, and pricing conventions. Establishes the financial context that motivates all subsequent quantitative methods.

Lesson 3 • Calculus and Linear Algebra Essentials

Reviews differentiation, integration, and matrix operations relevant to finance. Enables students to manipulate pricing formulas and portfolio equations.

Lesson 4 • Time Value of Money and Discounting

Establishes present value, compounding conventions, and yield concepts. Links classical finance theory to quantitative pricing frameworks.

Lesson 1 • Random Walks and Brownian Motion

Introduces discrete random walks and their continuous limit. Establishes Brownian motion as the canonical model for financial noise.

Lesson 2 • Stochastic Differential Equations

Defines SDEs and their solution techniques. Connects continuous-time dynamics to asset price models used in derivatives pricing.

Lesson 3 • Martingales and Change of Measure

Covers martingale theory and the Girsanov theorem. Enables risk-neutral pricing by transforming probability measures.

Lesson 1 • Exotic and Path-Dependent Options

Prices barrier, Asian, and lookback options analytically and numerically. Extends the core framework to non-standard payoff structures.

Lesson 2 • Black-Scholes Model and Formula

Derives the Black-Scholes PDE and closed-form option prices. Connects GBM dynamics to practical call and put valuation.

Lesson 3 • Interest Rate Derivatives Pricing

Values caps, floors, swaptions, and bond options using rate models. Bridges equity derivatives theory to fixed-income derivative markets.

Lesson 4 • Binomial and Lattice Models

Builds discrete-time pricing trees for European and American options. Reinforces no-arbitrage concepts with intuitive lattice structures.

Lesson 1 • Bond Pricing and Yield Measures

Computes bond prices from cash flows and derives yield metrics. Anchors fixed-income analysis in fundamental discounting mechanics.

Lesson 2 • Short-Rate and Affine Term Structure Models

Presents Vasicek, CIR, and Hull-White models for interest rate dynamics. Connects stochastic rate processes to bond pricing and hedging.

Lesson 3 • Credit Spreads and Risky Bonds

Incorporates default risk into bond pricing via spread and structural models. Extends risk-free term structure analysis to credit markets.

Lesson 4 • Duration, Convexity, and Sensitivity

Measures interest rate sensitivity using duration and convexity. Enables hedging and risk management of fixed-income portfolios.

Lesson 1 • Capital Asset Pricing Model

Derives CAPM equilibrium and the security market line. Links systematic risk to expected return for asset pricing and benchmarking.

Lesson 2 • Portfolio Optimization Techniques

Implements quadratic programming and robust optimization methods. Addresses estimation error and practical constraints in portfolio construction.

Lesson 3 • Mean-Variance Framework

Formalizes Markowitz portfolio theory using expected return and variance. Establishes the efficient frontier as the core optimization target.

Lesson 4 • Factor Models and Risk Decomposition

Extends CAPM to multi-factor models for return attribution. Enables granular risk decomposition across systematic and idiosyncratic sources.

Lesson 1 • Liquidity Risk and Market Microstructure

Measures bid-ask costs, market impact, and funding liquidity risk. Integrates liquidity considerations into risk-adjusted performance metrics.

Lesson 2 • Credit Risk Measurement

Quantifies probability of default, loss given default, and credit VaR. Connects fixed-income credit models to portfolio-level credit risk.

Lesson 3 • Expected Shortfall and Tail Risk

Introduces CVaR as a coherent alternative to VaR for tail risk. Addresses the limitations of VaR in capturing extreme loss distributions.

Lesson 4 • Value at Risk Methodologies

Derives VaR using historical, parametric, and Monte Carlo methods. Establishes the primary regulatory and internal risk measurement tool.

Lesson 1 • Implied Volatility and the Volatility Surface

Extracts implied volatility from market prices and maps the surface. Reveals the smile and skew patterns that Black-Scholes cannot explain.

Lesson 2 • Volatility Model Calibration

Fits stochastic volatility models to market option prices numerically. Develops practical calibration workflows used by derivatives desks.

Lesson 3 • Variance Swaps and Volatility Products

Prices variance swaps and volatility indices using replication arguments. Extends volatility modeling to tradable volatility instruments.

Lesson 4 • Stochastic Volatility Models

Presents Heston and SABR models with mean-reverting variance processes. Captures volatility clustering and smile dynamics observed in markets.

Lesson 1 • Optimal Execution and Market Impact

Applies Almgren-Chriss and VWAP frameworks to minimize execution costs. Bridges strategy alpha with net-of-cost realized performance.

Lesson 2 • Alpha Signal Research and Generation

Identifies and tests predictive signals from price, fundamental, and alternative data. Establishes a rigorous research process for alpha discovery.

Lesson 3 • Strategy Evaluation and Risk Controls

Assesses live strategy performance and enforces real-time risk limits. Completes the quantitative trading lifecycle from research to production.

Lesson 4 • Statistical Arbitrage Strategies

Builds pairs trading and cointegration-based strategies with entry and exit rules. Applies time series econometrics to market-neutral alpha generation.