A game theory analysis of options

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Modern option pricing theory emerged in the late sixties and early seventies, developed by F. Black, R. e. Merton, and M. Scholes as a tool for pricing and hedging option contracts and over-the-counter warrants. In their foundational paper, Black and Scholes suggested a broader applicability for their model, demonstrating that a levered firm's equity could be viewed as an option on the firm's value, enabling option valuation techniques for pricing. Merton expanded this concept a year later by illustrating how the default risk structure of corporate bonds could also be assessed using these techniques. Today, option pricing models are employed to price a wide array of financial instruments and guarantees, including deposit insurance and collateral, while also quantifying associated risks. Over time, option pricing has transitioned from specific models to a comprehensive analytical framework for understanding the production of financial contracts and their role in financial intermediation within a continuous time context. However, literature has largely overlooked the integration of game theory, specifically the strategic financial decisions of agents, into this framework. Dr. Alexandre Ziegler's thesis addresses this gap, leveraging the analytical advantages of continuous time models and closed-form valuation for derivatives.