Advanced Finance Theories

Advanced Finance Theories

by Ser-huang Poon

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Overview

For PhD finance courses in business schools, there is equal emphasis placed on mathematical rigour as well as economic reasoning. Advanced Finance Theories provides modern treatments to five key areas of finance theories in Merton's collection of continuous time work, viz. portfolio selection and capital market theory, optimum consumption and intertemporal portfolio selection, option pricing theory, contingent claim analysis of corporate finance, intertemporal CAPM, and complete market general equilibrium. Where appropriate, lectures notes are supplemented by other classical text such as Ingersoll (1987) and materials on stochastic calculus.

Product Details

ISBN-13: 9789814460378
Publisher: World Scientific Publishing Company, Incorporated
Publication date: 04/24/2018
Pages: 228
Product dimensions: 6.00(w) x 9.00(h) x 0.56(d)

Table of Contents

Preface vii

About the Author ix

Acknowledgements xi

Note for PhD Students xix

1 Utility Theory 1

1.1 Risk Aversion and Certainty Equivalent 3

2 Pricing Kernel and Stochastic Discount Factor 5

2.1 Arrow-Debreu State Prices 5

2.1.1 The pricing kernel, φi 6

2.1.2 Equilibrium model 8

2.2 Cochrane Two-period Consumption Problem 11

2.2.1 Stochastic discount factor 12

2.2.2 Further notation 13

2.2.3 Risk-free rate 13

2.2.4 Risk corrections 15

2.2.5 Idiosyncratic risk does not affect prices 16

2.3 Expected Return-Beta Representation 17

3 Risk Measures 19

3.1 One-period Portfolio Selection 19

3.2 Rothschild and Stiglitz "Strict" Risk Aversion 21

3.2.1 Efficient portfolio 22

3.2.2 Portfolio analysis 23

3.3 Merton's Risk Measures 26

3.3.1 Properties of Merton's risk measure bp 29

3.3.2 Relationship between bp and conditional expected return E[Zp|Ze] 33

3.3.3 Discussion 35

Exercises: Capital Market Theory, Risk Measures 38

4 Consumption and Portfolio Selection 39

4.1 Basic Set-up 39

4.2 One Risky and One Risk-Free Asset 41

4.2.1 The Bellman equation 41

4.2.2 Infinite time horizon 44

4.3 Constant Relative Risk Aversion 45

4.3.1 Solution for J 47

4.3.2 Solution for C and w 49

4.3.3 Economic interpretation 50

4.4 Constant Absolute Risk Aversion 51

4.4.1 Solve for J 51

4.4.2 Solve for C* and w* 53

4.4.3 Economic interpretation 53

4.5 Hyperbolic Absolute Risk Aversion (HARA) 54

4.5.1 Relationship with CRRA and CARA 54

4.5.2 Portfolio choice 55

4.5.3 Solution for J 56

4.5.4 Solve for C* and w* 58

4.6 Optimal Rules Under Finite Horizon 59

4.6.1 CRRA with finite horizon 61

4.6.2 CARA with finite horizon 61

Exercises: Intertemporal Portfolio Section 63

5 Optimum Demand and Mutual Fund Theorem 65

5.1 Asset Dynamics and the Budget Equation 65

5.2 The Equation of Optimality 66

5.3 Optimal Investment Weight and Special Cases 68

5.3.1 No risk-free asset 69

5.3.2 GBM and risk-free rate 71

5.3.3 Economic interpretation 72

5.4 Lognormality and Mutual Fund Theorem 73

5.4.1 "Separation" or "mutual-fund" theorem 73

5.4.2 Key assumptions and uniqueness 75

5.4.3 Tobin-Markowitz separation theorem 79

Exercises: Optimum Demand and Mutual Fund Separation 82

6 Mean-Variance Frontier 83

6.1 Mean-Variance Frontier 83

6.1.1 The Sharpe ratio 85

6.1.2 Calculating the mean-variance frontier 86

6.1.3 Decomposing the mean-variance frontier 89

6.1.4 Spanning the frontier 92

6.1.5 Hansen-Jagannathan bounds 93

7 Solving Black-Scholes with Fourier Transform 95

7.1 Option Pricing with Fourier Transform 95

7.1.1 Black-Scholes hedge portfolio 96

7.2 Black-Scholes Fundamental PDE 96

7.2.1 Fourier transform 97

7.2.2 Solution through transform method 98

8 Capital Structure Theory 101

8.1 Objective Function for the Firm 101

8.2 Partial Equilibrium One-period Model 103

8.2.1 Pricing kernel 103

8.2.2 Probability-cum-utility function 105

8.2.3 m assets 105

8.2.4 Introducing the concept of dQ 107

8.2.5 What is eητ? 107

8.3 Payoff of Risky Debt 108

8.4 Pricing Risky Debt 111

8.4.1 Solving the FPDE 112

8.5 Price of a Warrant 114

8.6 Convertible Bond 116

8.6.1 Reverse convertible 117

8.6.2 Call option enhanced reverse convertible 118

8.6.3 Policy implications 118

8.7 Bankruptcy Cost and Tax Benefit 120

8.7.1 Solution under time invariant 120

8.7.2 Protected debt covenant 121

8.7.3 Optimal capital structure 122

8.8 Deposit Insurance 126

Exercises: Capital Structure Theory 128

9 General Equilibrium 129

9.1 Firms and Securities 129

9.2 Individuals 130

9.3 Aggregate Demand 131

9.4 Market Portfolio 132

9.5 Security Market Line 134

9.6 Three-fund Separation 135

9.7 Empirical Application of CAPM 136

Exercises: General Equilibrium 138

10 Discontinuity in Continuous Time 141

10.1 Counting and Marked Point Process 141

10.2 Poisson Process 142

10.3 Constant Jump Size 145

10.3.1 Fundamental PDE with constant jump size 146

10.3.2 Market price of jump risk 149

10.3.3 European call price 150

10.3.4 Immediate ruin 151

10.4 Random Jump Size 152

10.4.1 When J has a lognormal distribution 153

10.5 Intertemporal Portfolio Selection with Jumps 154

10.5.1 Portfolio selection 156

10.5.2 Stock markets systemic and idiosyncratic risk 158

Exercises: Discontinuity in Continuous Time 160

11 Spanning and Capital Market Theories 163

11.1 Necessary Conditions for Non-trivial Spanning 164

11.2 Efficient Portfolio and Spanning 167

11.3 Market Portfolio Spanning and CAPM 176

11.4 Arbitrage Pricing Theory (APT) 183

11.5 Modigliani-Miller Hypothesis 184

11.6 Comment on Spanning 189

11.7 HARA 190

Exercises: Spanning & Capital Market Theories 192

Bibliography 193

Calculus Notes 195

Index 203

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