A Game Theory Analysis of Options

Modern option pricing theory was developed in the late sixties and early seventies by F. Black, R. e. Merton and M. Scholes as an analytical tool for pricing and hedging option contracts and over-the-counter warrants. How­ ever, already in the seminal paper by Black and Scholes, the applicability of the model was regarded as much broader. In the second part of their paper, the authors demonstrated that a levered firm's equity can be regarded as an option on the value of the firm, and thus can be priced by option valuation techniques. A year later, Merton showed how the default risk structure of cor­ porate bonds can be determined by option pricing techniques. Option pricing models are now used to price virtually the full range of financial instruments and financial guarantees such as deposit insurance and collateral, and to quantify the associated risks. Over the years, option pricing has evolved from a set of specific models to a general analytical framework for analyzing the production process of financial contracts and their function in the financial intermediation process in a continuous time framework. However, very few attempts have been made in the literature to integrate game theory aspects, i. e. strategic financial decisions of the agents, into the continuous time framework. This is the unique contribution of the thesis of Dr. Alexandre Ziegler. Benefiting from the analytical tractability of contin­ uous time models and the closed form valuation models for derivatives, Dr.

Contenu

1 Methodological Issues.- 1.1 Introduction.- 1.2 Game Theory Basics: Backward Induction and Subgame Perfection.- 1.3 Option Pricing Basics: The General Contingent Claim Equation.- 1.4 The Method of Game Theory Analysis of Options.- 1.5 When is the Method Appropriate?.- 1.5.1 The Link Between Option Value and Expected Utility.- 1.5.2 When Will the Option's Value be Correct?.- 1.6 What Kind of Problems is the Method Particularly Suited for?.- 1.7 An Example: Determining the Price of a Perpetual Put Option.- 1.7.1 Step 1: Structure of the Game.- 1.7.2 Step 2: Valuing the Option for a Given ExerciseStrategy.- 1.7.3 Step 3: Solving the Game.- 1.7.4 The Solution.- 1.8 Outline of the Book.- 2 Credit and Collateral.- 2.1 Introduction.- 2.2 The Risk-Shifting Problem.- 2.2.1 The Model.- 2.2.2 Profit-Sharing Contracts Between Lender and Borrower.- 2.2.3 Developing an Incentive Contract.- 2.2.4 Renegotiation-Proof Incentive Contracts.- 2.2.5 The Feasible Renegotiation-Proof Incentive Contract.- 2.2.6 The Financing Decision.- 2.2.7 The Effect of Payouts.- 2.3 The Observability Problem.- 2.3.1 Costly State Verification.- 2.3.2 Collateral.- 2.4 Conclusion.- 3 Endogenous Bankruptcy and Capital Structure.- 3.1 Introduction.- 3.2 The Model.- 3.3 The Value of the Firm and its Securities.- 3.3.1 The Value of Debt.- 3.3.2 The Value of the Firm.- 3.3.3 The Value of Equity.- 3.4 The Effect of Capital Structure on the Firm's Bankruptcy Decision.- 3.4.1 The Equity Holders' Optimal Bankruptcy Choice.- 3.4.2 The Principal-Agent Problem of EndogenousBankruptcy.- 3.4.3 Measuring the Agency Cost of Debt Arising fromEndogenous Bankruptcy.- 3.5 The Investment Decision.- 3.5.1 Underinvestment.- 3.5.2 Risk-Shifting.- 3.5.3 Measuring the Agency Cost of Debt Arising from Risk-Shifting.- 3.5.4 The Incentive Effects of Loan Covenants.- 3.6 The Financing Decision.- 3.6.1 Optimal Capital Structure.- 3.6.2 Interest Payments vs. Increase in the Face Value of Debt.- 3.6.3 Equilibrium on the Credit Market.- 3.6.4 Capital Structure and the Expected Life of Companies.- 3.7 An Incentive Contract.- 3.7.1 Impact of the Effective Interest Rate.- 3.7.2 Impact of the Rate of Growth in Debt.- 3.8 The Impact of Payouts.- 3.8.1 The Value of the Firm and its Securities.- 3.8.2 The Bankruptcy Decision.- 3.8.3 The Effect of the Payout Rate on Equity Value.- 3.8.4 Effect of a Loan Covenant on the Optimal Payout Rate.- 3.9 Conclusion.- 4 Junior Debt.- 4.1 Introduction.- 4.2 The Model.- 4.3 The Value of the Firm and its Securities.- 4.3.1 The Value of Senior Debt.- 4.3.2 The Value of Junior Debt.- 4.3.3 The Value of the Firm.- 4.3.4 The Value of Equity.- 4.4 The Equity Holders' Optimal Bankruptcy Choice.- 4.5 The Firm's Decision to Issue Junior Debt.- 4.6 The Influence of Junior Debt on the Value of Senior Debt.- 4.6.1 On the Impossibility of Perfect Immunization.- 4.6.2 On the Impossibility of Immunization Against Negative Wealth Effects.- 4.7 Conclusion.- 5 Bank Runs.- 5.1 Introduction.- 5.2 The Model.- 5.3 The Depositors' Run Decision.- 5.4 Valuing the Bank's Equity.- 5.5 The Shareholders' Recapitalization Decision.- 5.6 The Bank's Investment Incentives when Bank Runs are Possible.- 5.7 The Bank's Funding Decision.- 5.7.1 On the Feasibility of Viable Financial Intermediation.- 5.7.2 Optimal Bank Capital when Asset Risk is Positive.- 5.7.3 Optimal Bank Capital with Zero Asset Risk.- 5.8 Determining the Equilibrium Deposit Spread.- 5.9 Conclusion.- 6 Deposit Insurance.- 6.1 Introduction.- 6.2 The Model.- 6.3 Valuing Deposit Insurance, Bank Equity and Social Welfare.- 6.3.1 The Cost of the Deposit Insurance Guarantee.- 6.3.2 The Value of Bank Equity.- 6.3.3 The Value of Social Welfare.- 6.4 The Guarantor's Liquidation Strategy and Social Welfare.- 6.4.1 Minimizing the Cost of the Guarantee.- 6.4.2 Maximizing Social Welfare.- 6.4.3 Can Deposit Insurance Enhance Social Welfare?.- 6.5 The Incentive Effects of Deposit Insurance.- 6.5.1 The Investment Decision.- 6.5.2 The Financing Decision.- 6.6 The Impact of Deposit Insurance on the Equilibrium Deposit Spread.- 6.7 Deposit Insurance with Liquidation Delays.- 6.8 Deposit Insurance with Unobservable Asset Value.- 6.8.1 A First Approach: Extending the Model of Chapter 3.- 6.8.2 Merton's Solution.- 6.9 Conclusion.- 7 Summary and Conclusion.- References.- List of Figures.- List of Symbols.