Mathematical Techniques in Finance : An Introduction

Cover -- Title Page -- Copyright -- Contents -- Preface -- Acknowledgments -- About the Author -- Acronyms -- CHAPTER 1 Finance -- 1.1 Follow the Money -- 1.2 Financial Markets and Participants -- 1.3 Quantitative Finance -- CHAPTER 2 Rates, Yields, Bond Math -- 2.1 Interest Rates -- 2.1.1 Fractional Periods -- 2.1.2 Continuous Compounding -- 2.1.3 Discount Factor, PV, FV -- 2.1.4 Yield, Internal Rate of Return -- 2.2 Arbitrage, Law of One Price -- 2.3 Price‐Yield Formula -- 2.3.1 Clean Price -- 2.3.2 Zero‐Coupon Bond -- 2.3.3 Annuity -- 2.3.4 Fractional Years, Day Counts -- 2.3.5 U.S. Treasury Securities -- 2.4 Solving for Yield: Root Search -- 2.4.1 Newton‐Raphson Method -- 2.4.2 Bisection Method -- 2.5 Price Risk -- 2.5.1 PV01, PVBP -- 2.5.2 Convexity -- 2.5.3 Taylor Series Expansion -- 2.5.4 Expansion Around C -- 2.5.5 Numerical Derivatives -- 2.6 Level Pay Loan -- 2.6.1 Interest and Principal Payments -- 2.6.2 Average Life -- 2.6.3 Pool of Loans -- 2.6.4 Prepayments -- 2.6.5 Negative Convexity -- 2.7 Yield Curve -- 2.7.1 Bootstrap Method -- 2.7.2 Interpolation Method -- 2.7.3 Rich/Cheap Analysis -- 2.7.4 Yield Curve Trades -- Exercises -- Python Projects -- CHAPTER 3 Investment Theory -- 3.1 Utility Theory -- 3.1.1 Risk Appetite -- 3.1.2 Risk versus Uncertainty, Ranking -- 3.1.3 Utility Theory Axioms -- 3.1.4 Certainty‐Equivalent -- 3.1.5 X‐ARRA -- 3.2 Portfolio Selection -- 3.2.1 Asset Allocation -- 3.2.2 Markowitz Mean‐Variance Portfolio Theory -- 3.2.3 Risky Assets -- 3.2.4 Portfolio Risk -- 3.2.5 Minimum Variance Portfolio -- 3.2.6 Leverage, Short Sales -- 3.2.7 Multiple Risky Assets -- 3.2.8 Efficient Frontier -- 3.2.9 Minimum Variance Frontier -- 3.2.10 Separation: Two‐Fund Theorem -- 3.2.11 Risk‐Free Asset -- 3.2.12 Capital Market Line -- 3.2.13 Market Portfolio -- 3.3 Capital Asset Pricing Model -- 3.3.1 CAPM Pricing.