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Book Review: "A Game Theory of Analysis of Options: Corporate Finance and Financial Intermediation in Continuous Time", Alexandre Ziegler

“A Game Theory Analysis of Options” is a revised version of Alexandre Ziegler dissertation submitted to the University of St. Gallen, Switzerland. The book provides a stimulating and innovative approach to problems in options management and corporate finance. Given a financial asset, (a perpetual call option, deposit insurance, junior debt and so on), a leader-follower game is constructed based on the theoretical pricing model of such assets. The solution of these games provides a solution to some corporate finance problems expressed in terms of the model-game parameters. The book raises a number of issues and problems that are important for the reader to be aware of however. These issues and problems can stimulate further research, bridging the gap between financial options theory and management and applied game theory. The book is organized in a first introductory chapter which summarizes the essential elements of the approach the book assumes throughout subsequent chapters. In Chapter 1, a brief (unfortunately insufficient) introduction to game theory is outlined and a leader-follower game is considered based on a perpetual call option. This game essentially outlines the procedure used throughout the book in the context of various and interesting finance problems. The leader-follower game is set in the following format. Given a lognormal underlying stock process, the derived call option price is determined by an optimal exercise (stopping) time at which the stock reaches a given price (decision) level. At this optimal price (which assumes that markets are complete) the option is exercised by the option holder. The option issuer is now assumed to be a leader (fully informed) in a game where the option buyer (and subsequently holder) is a follower. In this (Stackelberg) game, the option issuer is presumed to have full knowledge of the market response and therefore he selects a unique (in pure strategies) exercise price. Each of the parties is assumed to benefit from the transaction which is defined in terms of parameters selection in a (partial) differential equation which calculates the option price.