A technical guide to mathematical finance

1. Introduction. 1.1. Notation and Formatting. 2. Basics. 2.1. Time Value of Money. 2.2. Continuous vs. Discrete Compounding. 3. Fixed Income. 3.1. Opportunity Cost of Capital. 3.2. Gordon Growth Model. 4. Time Series Processes. 4.1. Deterministic Processes. 4.2. Stochastic Processes. 5. Derivative Pricing. 5.1. No Arbitrage and Risk-Neutral Probabilities. 5.2. Black-Scholes-Merton Differential Equation. 5.3. The Black-Scholes-Merton Pricing Formula. 6. Modern Portfolio Theory & CAPM. 6.1. Linear Regression. 6.2. Modern Portfolio Theory. 7. Uncertainty & Value. 7.1. Jenson⁰́₉s Inequality. 7.2. Time-Declining Discount Rate. 8. Capital Structure Irrelevance. 8.1. Capital Budgeting. 9. Probability of Default. 9.1. Hazard Rates. 10. Appendix. 10.1. Rule of 72. 10.2. Quadratic Equation. 10.3. Forward Rates from Spot Rates. 10.4. Expected Future Spot Price.