Mathematical Techniques in Finance. Amir Sadr
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Table of Contents
1 Cover
5 Preface BACKGROUND BOOK STRUCTURE
8 Acronyms
9 CHAPTER 1: Finance 1.1 FOLLOW THE MONEY 1.2 FINANCIAL MARKETS AND PARTICIPANTS 1.3 QUANTITATIVE FINANCE
10 CHAPTER 2: Rates, Yields, Bond Math 2.1 INTEREST RATES 2.2 ARBITRAGE, LAW OF ONE PRICE 2.3 PRICE‐YIELD FORMULA 2.4 SOLVING FOR YIELD: ROOT SEARCH 2.5 PRICE RISK 2.6 LEVEL PAY LOAN 2.7 YIELD CURVE EXERCISES PYTHON PROJECTS
11 CHAPTER 3: Investment Theory 3.1 UTILITY THEORY 3.2 PORTFOLIO SELECTION 3.3 CAPITAL ASSET PRICING MODEL 3.4 FACTORS 3.5 MEAN‐VARIANCE EFFICIENCY AND UTILITY 3.6 INVESTMENTS IN PRACTICE REFERENCES EXERCISES PYTHON PROJECTS
12 CHAPTER 4: Forwards and Futures 4.1 FORWARDS 4.2 FUTURES CONTRACTS 4.3 STOCK DIVIDENDS 4.4 FORWARD FOREIGN CURRENCY EXCHANGE RATE 4.5 FORWARD INTEREST RATES REFERENCES EXERCISES
13 CHAPTER 5: Risk‐Neutral Valuation 5.1 CONTINGENT CLAIMS 5.2 BINOMIAL MODEL 5.3 FROM ONE TIME‐STEP TO TWO 5.4 RELATIVE PRICES REFERENCES EXERCISES
14 CHAPTER 6: Option Pricing 6.1 RANDOM WALK AND BROWNIAN MOTION 6.2 BLACK‐SCHOLES‐MERTON CALL FORMULA 6.3 IMPLIED VOLATILITY 6.4 GREEKS 6.5 DIFFUSIONS, ITO 6.6 CRR BINOMIAL MODEL 6.7 AMERICAN‐STYLE OPTIONS 6.8 PATH‐DEPENDENT OPTIONS 6.9 EUROPEAN OPTIONS IN PRACTICE REFERENCES EXERCISES PYTHON PROJECTS
15 CHAPTER 7: Interest Rate Derivatives 7.1 TERM STRUCTURE OF INTEREST RATES 7.2 INTEREST RATE SWAPS 7.3 INTEREST RATE DERIVATIVES 7.4 INTEREST RATE MODELS 7.5 BERMUDAN SWAPTIONS 7.6 TERM STRUCTURE MODELS 7.7 INTEREST RATE DERIVATIVES IN PRACTICE REFERENCES EXERCISES
16 APPENDIX A: Math and Probability Review A.1 CALCULUS AND DIFFERENTIATION RULES