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.

Integration of game theory aspects into the framework of continuous time finance Numerous figures allow the reader to visualize the results obtained in the formal mathematical analysis Includes supplementary material: sn.pub/extras

Klappentext

This book shows how to combine game theory and option pricing in order to analyze dynamic multiperson decision problems in continuous time and under uncertainty. The basic intuition of the method is to separate the problem of the valuation of payoffs from the analysis of strategic interactions. Whereas the former is to be handled using option pricing, the latter can be addressed by game theory. The text shows how both instruments can be combined and how game theory can be applied to complex problems of corporate finance and financial intermediation. Besides providing theoretical foundations and serving as a guide to stochastic game theory modelling in continuous time, the text contains numerous applications to the theory of corporate finance and financial intermediation, such as the design of debt contracts, capital structure choice, the structure of banking deposit contracts, and the incentive effects of deposit insurance. By combining arbitrage-free valuation techniques with strategic analysis, the game theory analysis of options actually provides the link between markets and organizations.

Inhalt
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?.- 1.6 What Kind of Problems is the Method Particularly Suited for?.- 1.7 An Example: Determining the Price of a Perpetual Put Option.- 1.8 Outline of the Book.- 2 Credit and Collateral.- 2.1 Introduction.- 2.2 The Risk-Shifting Problem.- 2.3 The Observability Problem.- 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.- 3.4 The Effect of Capital Structure on the Firm's Bankruptcy Decision.- 3.5 The Investment Decision.- 3.6 The Financing Decision.- 3.7 An Incentive Contract.- 3.8 The Impact of Payouts.- 3.9 Conclusion.- 4 Junior Debt.- 4.1 Introduction.- 4.2 The Model.- 4.3 The Value of the Firm and its Securities.- 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.- 4.7 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.- 5.8 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.- 6.4 The Guarantor's Liquidation Strategy and Social Welfare.- 6.5 The Incentive Effects of Deposit Insurance.- 6.6 The Impact of Deposit Insurance on theEquilibrium Deposit Spread.- 6.7 Deposit Insurance with Liquidation Delays.- 6.8 Deposit Insurance with Unobservable Asset Value.- 6.9 Conclusion.- 7 Summary and Conclusion.- References.- List of Figures.- List of Symbols.