📉 Finance II
Sources: MIT OCW 18.S096 · MIT OCW 15.450 (CC BY-NC-SA 4.0).
The math behind the prices. Stochastic calculus, derivative pricing, volatility modeling, and credit risk — with industry applications from Morgan Stanley.
| Chapter | |||
|---|---|---|---|
| 1. | Stochastic Processes | Random walks, Markov chains, and the probabilistic machinery prices live on. | 📉 |
| 2. | Ito Calculus | Brownian motion, Ito's lemma, stochastic differential equations. The calculus of noise. | 📉 |
| 3. | Black-Scholes Derivation | Risk-neutral valuation, the replicating portfolio argument, and the PDE. | 📉 |
| 4. | Monte Carlo Methods | Simulating prices to price derivatives. Variance reduction, convergence, path-dependent options. | 📉 |
| 5. | Volatility Modeling | GARCH, implied volatility surfaces, the smile, and why constant volatility is wrong. | 📉 |
| 6. | Time Series Analysis | Autoregression, stationarity, cointegration. Extracting signal from financial data. | 📉 |
| 7. | Factor Models | Fama-French, PCA on returns, risk decomposition beyond CAPM. | 📉 |
| 8. | Interest Rate Models | Vasicek, CIR, HJM framework. Modeling the term structure and pricing rate derivatives. | 📉 |
| 9. | Credit Risk | Default probability, credit spreads, ratings transitions, structural and reduced-form models. | 📉 |
| 10. | Credit Derivatives | CDS, CDOs, counterparty risk. The instruments that amplified 2008. | 📉 |
| 11. | Value at Risk | Measuring tail risk: historical simulation, parametric VaR, expected shortfall. | 📉 |
| 12. | Dynamic Portfolio Choice | Multi-period optimization, rebalancing, dynamic programming for long-horizon investors. | 📉 |
📺 Video lectures: MIT 18.S096: Topics in Mathematics with Applications in Finance
Neighbors
- 📈 Finance — prerequisite: TVM, portfolio theory, CAPM, options intro
- ∫ Calculus — derivatives and integrals underpin everything here
- 🎰 Probability — stochastic processes build on measure theory
- 📊 Statistics — econometric methods for estimation and testing