A game theory analysis of options

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Modern option pricing theory, developed in the late sixties and early seventies by F. Black, R. C. Merton, and M. Scholes, serves as an analytical tool for pricing and hedging options and over-the-counter warrants. In their foundational paper, Black and Scholes suggested that the model's applicability extends beyond options, illustrating that a levered firm's equity can be viewed as an option on the firm's value, allowing for pricing through option valuation techniques. Merton further demonstrated how the default risk structure of corporate bonds could be analyzed using these techniques. Today, option pricing models are employed to price a wide array of financial instruments and guarantees, such as deposit insurance and collateral, while also quantifying associated risks. Over time, the field has transitioned from specific models to a comprehensive analytical framework for understanding financial contracts and their roles in financial intermediation within a continuous time context. Notably, there has been little integration of game theory elements—specifically, the strategic financial decisions of agents—into this continuous time framework. This gap is addressed in Dr. Alexandre Ziegler's thesis, which leverages the analytical advantages of continuous time models and closed-form valuation for derivatives.