Description
A Technical Guide to Mathematical Finance covers those foundational mathematical topics most important to an aspiring or professional quant. The text goes beyond a simple recitation of methods and aims to impart a genuine understanding of the fundamental concepts underpinning most of the techniques and tools routinely used by those working in quantitative finance.
Features
- Suitable for professional quants and graduate students in finance, and mathematical/quantitative finance
- “Concept Refreshers” used throughout to provide pithy summaries of complex topics
- Step-by-step detail for formal proofs and mathematical descriptions
Table of Contents
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. Jenson’s 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.
