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
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.
Biography
Derek Zweig is the Chief Executive Officer and co-founder of Value Analytics, a data and analytics firm specializing in equity markets. Prior to founding Value Analytics, he worked as a capital markets risk analyst at a large regional bank where he specialized in market and counterparty risk. Along with his experience in risk, Derek spent much of his career valuing business interests and intangible assets of private and public companies. He is an active member of the CFA Institute and the Global Association of Risk Professionals. He has a graduate certificate in Financial Engineering from Columbia University, an M.S. in Applied Economics from Johns Hopkins University, and a B.S. in Finance from the Ohio State University. Derek regularly tutors children and young adults in mathematics, and enjoys rock climbing, pickup basketball and volleyball, and spending endless hours clowning around with his daughter.
