ISBN: 354020668X
TITLE: A Game Theory Analysis of Options
AUTHOR: Ziegler
TOC:

1 Methodological Issues 1
1.1 Introduction 1
1.2 Game Theory Basics: Backward Induction and Subgame Perfection 2
1.3 Option Pricing Basics: The General Contingent Claim Equation 5
1.4 The Method of Game Theory Analysis of Options 7
1.5 When is the Method Appropriate? 8
1.5.1 The Link Between Option Value and Expected Utility 9
1.5.2 When Will the Option's Value be Correct? 9
1.6 What Kind of Problems is the Method Particularly Suited for? 10
1.7 An Example: Determining the Price of a Perpetual Put Option 11
1.7.1 Step 1: Structure of the Game 11
1.7.2 Step 2: Valuing the Option for a Given Exercise Strategy 12
1.7.3 Step 3: Solving the Game 13
1.7.4 The Solution 15
1.8 Outline of the Book 16
2 Credit and Collateral 19
2.1 Introduction 19
2.2 The Risk-Shifting Problem 20
2.2.1 The Model 21
2.2.2 Profit-Sharing Contracts Between Lender and Borrower 22
2.2.3 Developing an Incentive Contract 23
2.2.4 Renegotiation-Proof Incentive Contracts 26
2.2.5 The Feasible Renegotiation-Proof Incentive Contract 28
2.2.6 The Financing Decision 29
2.2.7 The Effect of Payouts 29
2.3 The Observability Problem 31
2.3.1 Costly State Verification 31
2.3.2 Collateral 32
2.4 Conclusion 36
3 Endogenous Bankruptcy and Capital Structure 39
3.1 Introduction 39
3.2 The Model 41
3.3 The Value of the Firm and its Securities 43
3.3.1 The Value of Debt 43
3.3.2 The Value of the Firm 45
3.3.3 The Value of Equity 47
3.4 The Effect of Capital Structure on the Firm's Bankruptcy Decision 48
3.4.1 The Equity Holders' Optimal Bankruptcy Choice 48
3.4.2 The Principal-Agent Problem of Endogenous Bankruptcy 49
3.4.3 Measuring the Agency Cost of Debt Arising from Endogenous Bankruptcy 52
3.5 The Investment Decision 53
3.5.1 Underinvestment 53
3.5.2 Risk-Shifting 55
3.5.3 Measuring the Agency Cost of Debt Arising from Risk-Shifting 57
3.5.4 The Incentive Effects of Loan Covenants 58
3.6 The Financing Decision 59
3.6.1 Optimal Capital Structure 59
3.6.2 Interest Payments vs. Increase in the Face Value of Debt 62
3.6.3 Equilibrium on the Credit Market 64
3.6.4 Capital Structure and the Expected Life of Companies 66
3.7 An Incentive Contract 68
3.7.1 Impact of the Effective Interest Rate 6
3.7.2 Impact of the Rate of Growth in Debt 70
3.8 The Impact of Payouts 71
3.8.1 The Value of the Firm and its Securities 71
3.8.2 The Bankruptcy Decision 72
3.8.3 The Effect of the Payout Rate on Equity Value 73
3.8.4 Effect of a Loan Covenant on the Optimal Payout Rate 74
3.9 Conclusion 75
4 Junior Debt 77
4.1 Introduction 77
4.2 The Model 78
4.3 The Value of the Firm and its Securities 80
4.3.1 The Value of Senior Debt 80
4.3.2 The Value of Junior Debt 82
4.3.3 The Value of the Firm 84
4.3.4 The Value of Equity 85
4.4 The Equity Holders' Optimal Bankruptcy Choice 89
4.5 The Firm's Decision to Issue Junior Debt 91
4.6 The Influence of Junior Debt on the Value of Senior Debt 96
4.6.1 On the Impossibility of Perfect Immunization 96
4.6.2 On the Impossibility of Immunization Against Negative Wealth Effects 97
4.7 Conclusion 98
5 Bank Runs 101
5.1 Introduction 101
5.2 The Model 102
5.3 The Depositors' Run Decision 104
5.4 Valuing the Bank's Equity 106
5.5 The Shareholders' Recapitalization Decision 109
5.6 The Bank's Investment Incentives when Bank Runs are Possible 111
5.7 The Bank's Funding Decision 115
5.7.1 On the Feasibility of Viable Financial Intermediation 115
5.7.2 Optimal Bank Capital when Asset Risk is Positive 116
5.7.3 Optimal Bank Capital with Zero Asset Risk 120
5.8 Determining the Equilibrium Deposit Spread 120
5.9 Conclusion 121
6 Deposit Insurance 123
6.1 Introduction 123
6.2 The Model 124
6.3 Valuing Deposit Insurance, Bank Equity and Social Welfare 126
6.3.1 The Cost of the Deposit Insurance Guarantee 126
6.3.2 The Value of Bank Equity 127
6.3.3 The Value of Social Welfare 128
6.4 The Guarantor's Liquidation Strategy and Social Welfare 129
6.4.1 Minimizing the Cost of the Guarantee 129
6.4.2 Maximizing Social Welfare 130
6.4.3 Can Deposit Insurance Enhance Social Welfare? 130
6.5 The Incentive Effects of Deposit Insurance 133
6.5.1 The Investment Decision 133
6.5.2 The Financing Decision 136
6.6 The Impact of Deposit Insurance on the Equilibrium Deposit Spread 137
6.7 Deposit Insurance with Liquidation Delays 138
6.8 Deposit Insurance with Unobservable Asset Value 140
6.8.1 First Approach: Extending the Model of Chapter 3. 141
6.8.2 Merton's Solution 146
6.9 Conclusion 152
7 Summary and Conclusion 155
References 161
List of Figures 167
List of Symbols 169
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