Introduction To Quantitative Finance, An: A Three-principle Approach

by Christopher Hian-ann Ting

Overview

This concise textbook provides a unique framework to introduce Quantitative Finance to advanced undergraduate and beginning postgraduate students. Inspired by Newton's three laws of motion, three principles of Quantitative Finance are proposed to help practitioners also to understand the pricing of plain vanilla derivatives and fixed income securities.The book provides a refreshing perspective on Box's thesis that 'all models are wrong, but some are useful.' Being practice- and market-oriented, the author focuses on financial derivatives that matter most to practitioners.The three principles of Quantitative Finance serve as buoys for navigating the treacherous waters of hypotheses, models, and gaps between theory and practice. The author shows that a risk-based parsimonious model for modeling the shape of the yield curve, the arbitrage-free properties of options, the Black-Scholes and binomial pricing models, even the capital asset pricing model and the Modigliani-Miller propositions can be obtained systematically by applying the normative principles of Quantitative Finance.

Product Details

ISBN-13:	9789814704304
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	11/04/2015
Pages:	272
Product dimensions:	6.10(w) x 9.20(h) x 0.80(d)

Table of Contents

Foreword xiii

Preface xv

About the Author xix

Acknowledgments xxi

Notations xxiii

1 Introduction 1

1.1 A Brief History of Quantitative Finance 1

1.2 The 2008 Global Financial Crisis and Quantitative Finance 4

1.3 Fallacy of Prediction: White Kiwi 6

1.4 Beat the Market 9

1.5 Topics and Prospects of Quantitative Finance 12

1.6 Exercises 16

2 Brief Introduction to Four Major Asset Classes 21

2.1 Introduction 21

2.2 Stocks 22

2.3 Currencies 25

2.4 Commodities 29

2.5 Fixed Income 32

2.6 Other Investments 38

2.7 Exercises 39

3 Principles of Quantitative Finance 47

3.1 Introduction 47

3.2 Uncertainty and Risk 48

3.3 Principles of Quantitative Finance 50

3.3.1 First principle: Return is fixed in the absence of risk 50

3.3.2 Second principle: Expected return is directly proportional to risk 51

3.3.3 Third principle: Every willing buyer has a willing seller 55

3.4 Relative Valuation 59

3.5 An Application of the Principles of Quantitative Finance 62

3.6 Violations of Three Principles? 65

3.7 Principles versus Models 68

3.8 Physics Envy? 69

3.9 Market Friction 73

3.10 Exercises 75

4 Interest Rates 79

4.1 Introduction 79

4.2 Compounding Schemes 80

4.3 Zero-Coupon Yield Curve and Risks 82

4.3.1 Zero-coupon bonds and interest rate risks 83

4.3.2 Gurkaynak-Sack-Wright (GSW) dataset 87

4.3.3 Downward-sloping yield curve 88

4.3.4 U-shape and hump-shape yield curves 91

4.4 Interest Rate Risk and Bond Return 94

4.4.1 Return from the passage of time 95

4.4.2 Return due to the change in interest rate 96

4.5 Interest Rate Risk and the Yield Curve Shape 98

4.5.1 A model of long-term risks 99

4.5.2 A model of short-term risks 102

4.5.3 Summary of a tale of long-and short-term risks 104

4.6 Liquidity Risk 107

4.7 Credit Risk 108

4.8 Exercises 110

5 Derivatives with Linear Payoffs 113

5.1 Introduction 113

5.1.1 Linear payoffs 114

5.1.2 Nonlinear payoffs 115

5.2 Forward Forex Rate 116

5.2.1 Interest rate parity 117

5.2.2 Forward FX rates in practice 119

5.2.3 Non-Deliverable Forward (NDF) 120

5.3 Implied Forward Interest Rate 121

5.4 Forward Rate Agreement 122

5.5 Interest Rate Swap 126

5.6 Cross-Currency Interest Rate Swap (CIRS) 129

5.7 Discount Factors in Practice 130

5.8 Exercises 135

6 Derivatives with Nonlinear Payoffs 137

6.1 Introduction 137

6.2 European and American Puts and Calls 139

6.3 Overall Shape of European Call Option Price Function 142

6.3.1 Monotonous with respect to the strike price 142

6.3.2 Lower and upper bounds for the slope 143

6.3.3 Convexity 145

6.4 Overall Shape of European Put Option Price Function 147

6.4.1 Put option monotonicity and slope 147

6.4.2 Put option convexity 149

6.4.3 Summary 151

6.5 Bounds of European Option Price 153

6.5.1 Bounds on call prices 153

6.5.2 Bounds on put prices 154

6.5.3 Summary 156

6.6 Put-Call Parity 156

6.6.1 Implied forward price 158

6.6.2 Early exercise of American option 159

6.6.3 The Modigliani-Miller Proposition I 161

6.7 Box Spread Parity 163

6.8 Put-Call Inequalities for American Options 167

6.9 Exercises 170

7 Binomial Models 173

7.1 Introduction 173

7.2 Random Walk 175

7.3 One-Period Option Pricing 178

7.3.1 Pricing 179

7.3.2 Risk-neutral probability 182

7.4 Binomial Option Pricing 184

7.4.1 Replication of option's payoff 185

7.4.2 Multi-period generalization 186

7.4.3 Implementation of binomial option pricing model 188

7.4.4 A numerical example of binomial option pricing 189

7.5 From Binomial to Normal 191

7.5.1 Binomial probability 191

7.5.2 Normal probability density function 194

7.6 From Binomial to Black-Scholes 197

7.6.1 Probability of in-the-money Φ (d₂) 198

7.6.2 Probability of in-the-money Φ (d₁) 201

7.6.3 Numerical comparison to the binomial pricing model 204

7.7 Exercises 205

8 The Black-Scholes Model 207

8.1 Introduction 207

8.2 Einstein's Theory of Brownian Motion 208

8.3 Bachelier's Probability Law 210

8.4 Mathematical Brownian Motion 214

8.5 Itô Calculus 217

8.6 Black-Scholes Equation 220

8.7 Black-Scholes Equation is the Heat Equation 223

8.8 Solution of the Heat Equation 225

8.9 Solution of the Black-Scholes Equation 226

8.10 The Derman-Taleb Approach to Option Pricing 231

8.11 Exercises 234

Epilogue 237

Bibliography 241

Index 245