Mathematical Techniques in Finance - An Introduction

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.

List of contents

Preface xiii
 
Background xiii
 
Book Structure xiv
 
Bonds xiv
 
Stocks, Investments xv
 
Forwards, Futures xv
 
Risk-Neutral Option Pricing xv
 
Interest Rate Derivatives xvi
 
Problems and Python Projects xvi
 
Acknowledgments xix
 
Acronyms xxiii
 
1 Finance 1
 
1.1 Follow the Money 1
 
1.2 Financial Markets and Participants 2
 
1.3 Quantitative Finance 4
 
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 16
 
2.3.3 Annuity 17
 
2.3.4 Fractional Years, Day Counts 17
 
2.3.5 US Treasury Securities 19
 
2.4 Solving for Yield: Root Search 20
 
2.4.1 Newton-Raphson Method 21
 
2.4.2 Bisection Method 22
 
2.5 Price Risk 22
 
2.5.1 PV01, PVBP 22
 
2.5.2 Convexity 23
 
2.5.3 Taylor Series Expansion 24
 
2.5.4 Expansion Around C 26
 
2.5.5 Numerical Derivatives 27
 
2.6 Level Pay Loan 27
 
2.6.1 Interest and Principal Payments 29
 
2.6.2 Average Life 30
 
2.6.3 Pool of Loans 30
 
2.6.4 Prepayments 31
 
2.6.5 Negative Convexity 33
 
2.7 Yield Curve 35
 
2.7.1 Bootstrap Method 36
 
2.7.2 Interpolation Method 36
 
2.7.3 Rich/Cheap Analysis 38
 
2.7.4 Yield Curve Trades 38
 
Problems 39
 
Python Projects 46
 
3 Investment Theory 53
 
3.1 Utility Theory 54
 
3.1.1 Risk Appetite 54
 
3.1.2 Risk versus Uncertainty, Ranking 56
 
3.1.3 Utility Theory Axioms 58
 
3.1.4 Certainty-Equivalent 58
 
3.1.5 X-ARRA 60
 
3.2 Portfolio Selection 62
 
3.2.1 Asset Allocation 62
 
3.2.2 Markowitz Mean-Variance Theory 63
 
3.2.3 Risky Assets 64
 
3.2.4 Portfolio Risk 64
 
3.2.5 Minimum Variance Portfolio 65
 
3.2.6 Leverage, Short Sales 67
 
3.2.7 Multiple Risky Assets 69
 
3.2.8 Efficient Frontier 73
 
3.2.9 Minimum Variance Frontier 73
 
3.2.10 Separation: Two Fund Theorem 75
 
3.2.11 Risk-Free Asset 76
 
3.2.12 Capital Market Line 76
 
3.2.13 Market Portfolio 77
 
3.3 Capital Asset Pricing Model 78
 
3.3.1 CAPM Pricing 81
 
3.3.2 Systematic and Diversifiable Risk 81
 
3.4 Factors 82
 
3.4.1 Arbitrage Pricing Theory 82
 
3.4.2 Fama-French Factors 84
 
3.4.3 Factor Investing 85
 
3.4.4 PCA 85
 
3.5 Mean-Variance Efficiency and Utility 87
 
3.5.1 Parabolic Utility 89
 
3.5.2 Jointly Normal Returns 89
 
3.6 Investments in Practice 90
 
3.6.1 Re-balancing 91
 
3.6.2 Performance Measures 91
 
3.6.3 Z-Scores, Mean-Reversion, Rich-Cheap 92
 
3.6.4 Pairs Trading 92
 
3.6.5 Risk Management 94
 
Bibliography 96
 
Problems 98
 
Python Projects 103
 
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 113
 
4.2.1 Futures versus Forwards 115
 
4.2.2 Zero-Cost, Leverage 116
&

About the author

AMIR SADR, Ph.D. is a highly sought-after expert in fixed income and interest rate derivatives. He is a university lecturer at NYU Courant and a consultant to banks and hedge funds, with a current focus on crypto derivatives. He has held senior management roles in quantitative research and trading at major banks and hedge funds including Morgan Stanley, Greenwich Capital, and Brevan Howard.

Summary

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.

Product details

• Authors: a Sadr, Amir Sadr, Amir (Oklahoma State University Sadr, SADR AMIR
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 30.04.2022
• EAN: 9781119838401
• ISBN: 978-1-119-83840-1
• No. of pages: 272
• Series: Wiley Finance; Wiley Finance Editions
• Subjects: Social sciences, law, business > Business > Business administration; Finance & Investments, Finanz- u. Anlagewesen, Institutionelle Finanzplanung, Institutional & Corporate Finance