## A Game Theory Analysis of Options: Corporate Finance and Financial Intermediation in Continuous TimeModern 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. |

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### Contents

Methodological Issues | 1 |

Backward Induction and Subgame Perfection | 2 |

The General Contingent Claim Equation | 5 |

14 The Method of Game Theory Analysis of Options | 7 |

15 When is the Method Appropriate? | 8 |

151 The Link Between Option Value and Expected Utility | 9 |

16 What Kind of Problems is the Method Particularly Suited for? | 10 |

Determining the Price of a Perpetual Put Option | 11 |

383 The Effect of the Payout Rate on Equity Value | 73 |

384 Effect of a Loan Covenant on the Optimal Payout Rate | 74 |

39 Conclusion | 75 |

Junior Debt | 77 |

42 The Model | 78 |

43 The Value of the Firm and its Securities | 80 |

432 The Value of Junior Debt | 82 |

433 The Value of the Firm | 84 |

Valuing the Option for a Given Exercise Strategy | 12 |

Solving the Game | 13 |

174 The Solution | 15 |

18 Outline of the Book | 16 |

Credit and Collateral | 19 |

22 The RiskShifting Problem | 20 |

221 The Model | 21 |

222 ProfitSharing Contracts Between Lender and Borrower | 22 |

223 Developing an Incentive Contract | 23 |

224 RenegotiationProof Incentive Contracts | 26 |

225 The Feasible RenegotiationProof Incentive Contract | 28 |

226 The Financing Decision | 29 |

23 The Observability Problem | 31 |

232 Collateral | 32 |

24 Conclusion | 36 |

Endogenous Bankruptcy and Capital Structure | 39 |

32 The Model | 41 |

33 The Value of the Firm and its Securities | 43 |

332 The Value of the Firm | 45 |

333 The Value of Equity | 47 |

34 The Effect of Capital Structure on the Firms Bankruptcy Decision | 48 |

342 The PrincipalAgent Problem of Endogenous Bankruptcy | 49 |

343 Measuring the Agency Cost of Debt Arising from Endogenous Bankruptcy | 52 |

35 The Investment Decision | 53 |

352 RiskShifting | 55 |

353 Measuring the Agency Cost of Debt Arising from RiskShifting | 57 |

354 The Incentive Effects of Loan Covenants | 58 |

36 The Financing Decision | 59 |

362 Interest Payments vs Increase in the Face Value of Debt | 62 |

363 Equilibrium on the Credit Market | 64 |

364 Capital Structure and the Expected Life of Companies | 66 |

37 An Incentive Contract | 68 |

371 Impact of the Effective Interest Rate | 69 |

372 Impact of the Rate of Growth in Debt | 70 |

38 The Impact of Payouts | 71 |

382 The Bankruptcy Decision | 72 |

434 The Value of Equity | 85 |

44 The Equity Holders Optimal Bankruptcy Choice | 89 |

45 The Firms Decision to Issue Junior Debt | 91 |

46 The Influence of Junior Debt on the Value of Senior Debt | 96 |

462 On the Impossibility of Immunization Against Negative Wealth Effects | 97 |

47 Conclusion | 98 |

Bank Runs | 101 |

52 The Model | 102 |

53 The Depositors Run Decision | 104 |

54 Valuing the Banks Equity | 106 |

55 The Shareholders Recapitalization Decision | 109 |

56 The Banks Investment Incentives when Bank Runs are Possible | 111 |

57 The Banks Funding Decision | 115 |

572 Optimal Bank Capital when Asset Risk is Positive | 116 |

573 Optimal Bank Capital with Zero Asset Risk | 120 |

59 Conclusion | 121 |

Deposit Insurance | 123 |

62 The Model | 124 |

63 Valuing Deposit Insurance Bank Equity and Social Welfare | 126 |

632 The Value of Bank Equity | 127 |

633 The Value of Social Welfare | 128 |

64 The Guarantors Liquidation Strategy and Social Welfare | 129 |

642 Maximizing Social Welfare | 130 |

65 The Incentive Effects of Deposit Insurance | 133 |

652 The Financing Decision | 136 |

66 The Impact of Deposit Insurance on the Equilibrium Deposit Spread | 137 |

67 Deposit Insurance with Liquidation Delays | 138 |

68 Deposit Insurance with Unobservable Asset Value | 140 |

Extending the Model of Chapter 3 | 141 |

682 Mertons Solution | 146 |

69 Conclusion | 152 |

Summary and Conclusion | 155 |

161 | |

List of Figures | 167 |

List of Symbols | 169 |

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A game theory analysis of options: corporate finance and financial ... Alexandre Ziegler No preview available - 2010 |

### Common terms and phrases

a)SB agency cost amount analysis of options analyze asset risk asset value SB assets-to-deposits ratio backward induction bank runs bank's assets bankruptcy costs bankruptcy decision bankruptcy-triggering asset value borrower's boundary conditions call option capital structure Chap chapter choose collateral contingent claims cost of debt deposit insurance depositors endogenous bankruptcy equilibrium deposit spread equity holders equity value event of bankruptcy expected profit face value financial intermediation following parameter values function game theory analysis game tree geometric Brownian motion given guarantor impact incentive contract initial interest payments interest rate investment decision issue junior debt junior debt issue lender and borrower liquidate the bank liquidation costs liquidation-triggering maximize option pricing payoff payout rate Player principal-agent problem renegotiation-proof result risk-free Risk-free interest rate risk-neutral probability risk-shifting incentive risk-shifting problem Sect senior debt holders social welfare Solving underlying asset value of bank value of debt value of equity value of senior Wiener process yields