An Introduction
Buch, Englisch, 272 Seiten, Format (B × H): 162 mm x 237 mm, Gewicht: 458 g
ISBN: 978-1-119-83840-1
Verlag: Wiley
Explore the foundations of modern finance with this intuitive mathematical guide
In Mathematical Techniques in Finance: An Introduction, distinguished finance professional Amir Sadr delivers an essential and practical guide to the mathematical foundations of various areas of finance, including corporate finance, investments, risk management, and more.
Readers will discover a wealth of accessible information that reveals the underpinnings of business and finance. You’ll learn about: - Investment theory, including utility theory, mean-variance theory and asset allocation, and the Capital Asset Pricing Model
- Derivatives, including forwards, options, the random walk, and Brownian Motion
- Interest rate curves, including yield curves, interest rate swap curves, and interest rate derivatives
Complete with math reviews, useful Excel functions, and a glossary of financial terms, Mathematical Techniques in Finance: An Introduction is required reading for students and professionals in finance.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Preface xiii
Acknowledgments xix
About the Author xxi
Acronyms xxiii
Chapter 1 Finance 1
1.1 Follow the Money 1
1.2 Financial Markets and Participants 3
1.3 Quantitative Finance 5
Chapter 2 Rates, Yields, Bond Math 7
2.1 Interest Rates 7
2.1.1 Fractional Periods 8
2.1.2 Continuous Compounding 9
2.1.3 Discount Factor, PV, FV 9
2.1.4 Yield, Internal Rate of Return 10
2.2 Arbitrage, Law of One Price 11
2.3 Price-Yield Formula 12
2.3.1 Clean Price 15
2.3.2 Zero-Coupon Bond 17
2.3.3 Annuity 17
2.3.4 Fractional Years, Day Counts 19
2.3.5 U.S. Treasury Securities 20
2.4 Solving for Yield: Root Search 21
2.4.1 Newton-Raphson Method 21
2.4.2 Bisection Method 21
2.5 Price Risk 22
2.5.1 Pv01, Pvbp 23
2.5.2 Convexity 24
2.5.3 Taylor Series Expansion 25
2.5.4 Expansion Around c 27
2.5.5 Numerical Derivatives 27
2.6 Level Pay Loan 28
2.6.1 Interest and Principal Payments 30
2.6.2 Average Life 31
2.6.3 Pool of Loans 32
2.6.4 Prepayments 32
2.6.5 Negative Convexity 34
2.7 Yield Curve 36
2.7.1 Bootstrap Method 37
2.7.2 Interpolation Method 37
2.7.3 Rich/Cheap Analysis 39
2.7.4 Yield Curve Trades 40
Exercises 41
Python Projects 48
Chapter 3 Investment Theory 55
3.1 Utility Theory 56
3.1.1 Risk Appetite 57
3.1.2 Risk versus Uncertainty, Ranking 58
3.1.3 Utility Theory Axioms 59
3.1.4 Certainty-Equivalent 61
3.1.5 X-arra 63
3.2 Portfolio Selection 64
3.2.1 Asset Allocation 65
3.2.2 Markowitz Mean-Variance Portfolio Theory 65
3.2.3 Risky Assets 66
3.2.4 Portfolio Risk 66
3.2.5 Minimum Variance Portfolio 68
3.2.6 Leverage, Short Sales 71
3.2.7 Multiple Risky Assets 71
3.2.8 Efficient Frontier 75
3.2.9 Minimum Variance Frontier 76
3.2.10 Separation: Two-Fund Theorem 78
3.2.11 Risk-Free Asset 79
3.2.12 Capital Market Line 79
3.2.13 Market Portfolio 80
3.3 Capital Asset Pricing Model 81
3.3.1 CAPM Pricing 84
3.3.2 Systematic and Diversifiable Risk 84
3.4 Factors 85
3.4.1 Arbitrage Pricing Theory 85
3.4.2 Fama-French Factors 87
3.4.3 Factor Investing 88
3.4.4 Pca 88
3.5 Mean-Variance Efficiency and Utility 90
3.5.1 Parabolic Utility 91
3.5.2 Jointly Normal Returns 92
3.6 Investments in Practice 93
3.6.1 Rebalancing 93
3.6.2 Performance Measures 94
3.6.3 Z-Scores, Mean-Reversion, Rich-Cheap 95
3.6.4 Pairs Trading 95
3.6.5 Risk Management 97
3.6.5.1 Gambler’s Ruin 97
3.6.5.2 Kelly’s Ratio 98
References 99
Exercises 100
Python Projects 106
Chapter 4 Forwards and Futures 109
4.1 Forwards 109
4.1.1 Forward Price 110
4.1.2 Cash and Carry 111
4.1.3 Interim Cash Flows 111
4.1.4 Valuation of Forwards 111
4.1.5 Forward Curve 112
4.2 Futures Contracts 114
4.2.1 Futures versus Forwards 115
4.2.2 Zero-Cost, Leverage 116
4.2.3 Mark-to-Market Loss 116
4.3 Stock Dividends 117
4.4 Forward Foreign Currency Exchange Rate 117
4.5 Forward Interest Rates 119
References 120
Exercises 120
Chapter 5 Risk-Neutral Valuation 125
5.1 Contingent Claims 125
5.2 Binomial Model 127
5.2.1 Probability-Free Pricing 130
5.2.2 No Arbitrage 130
5.2.3 Risk-Neutrality 131
5.3 From One Time-Step to Two 132
5.3.1 Self-Financing, Dynamic Hedging 134
5.3.2 Iterated Expectation 135
5.4 Relative Prices 137
5.4.1 Risk-Neutral Valuation 138
5.4.2 Fundamental Theorems of Asset Pricing 140
References 140
Exercises 141
Chapter 6 Option Pricing 143
6.1 Random Walk and Brownian Motion 143
6.1.1 Random Walk 143
6.1.2 Brownian Motion 144
6.1.3 Lognormal Distribution, Geometric Brownian Motion 145
6.2 Black-Scholes-Merton Call Formula 145
6.2.1 Put-Call Parity 151
6.2.2 Black’s Formula: Options on Forwards 152
6.2.3 Call Is All You Need 153
6.3 Implied Volatility 154
6.3.1 Skews, Smiles 155
6.4 Greeks 156
6.4.1 Greeks Formulas 157
6.4.2 Gamma versus Theta 157
6.4.3 Delta, Gamma versus Time 160
6.5 Diffusions, Ito 161
6.5.1 Black-Scholes-Merton PDE 162
6.5.2 Call Formula and Heat Equation 163
6.6 CRR Binomial Model 165
6.6.1 CRR Greeks 167
6.7 American-Style Options 167
6.7.1 American Call Options 168
6.7.2 Backward Induction 169
6.8 Path-Dependent Options 170
6.9 European Options in Practice 173
References 173
Exercises 174
Python Projects 179
Chapter 7 Interest Rate Derivatives 187
7.1 Term Structure of Interest Rates 187
7.1.1 Zero Curve 187
7.1.2 Forward Rate Curve 188
7.2 Interest Rate Swaps 189
7.2.1 Swap Valuation 190
7.2.2 Swap = Bone - 100% 193
7.2.3 Discounting the Forwards 193
7.2.4 Swap Rate as Average Forward Rate 193
7.3 Interest Rate Derivatives 194
7.3.1 Black’s Normal Model 194
7.3.2 Caps and Floors 196
7.3.3 European Swaptions 197
7.3.4 Constant Maturity Swaps 200
7.4 Interest Rate Models 200
7.4.1 Money Market Account, Short Rate 201
7.4.2 Short Rate Models 202
7.4.3 Mean Reversion, Vasicek and Hull-White Models 202
7.4.4 Short Rate Lattice Model 204
7.4.5 Pure Securities 206
7.5 Bermudan Swaptions 208
7.6 Term Structure Models 211
7.7 Interest Rate Derivatives in Practice 212
7.7.1 Interest Rate Risk 212
7.7.2 Value at Risk (VaR) 213
References 213
Exercises 214
Appendix A Math and Probability Review 217
A. 1 Calculus and Differentiation Rules 217
A.2 Probability Review 218
A.3 Linear Regression Analysis 225
Appendix B Useful Excel Functions 229
About the Companion Website 231
Index 233
