Game-Theoretical Approach to Pricing a Perpetual Option

Goal

To review relevant literature and simulate a basic model that provides an alternative approach to the standard methods of pricing perpetual options.

Table of Contents

1. Introduction

   • Motivation

2. Basics

   • Option Pricing
     • Call Option
     • Put Option
     • Boundary Conditions
   • Game Theory
     • Fundamentals of Game Theory
     • Setting up the Game

3. Game-Theoretical Modeling of Option Pricing

   • Methodological Approach
     • Three-Step Procedure
   • Application on an Example
     • Step 1
     • Step 2
     • Step 3
   • Example Simulation (Code located in src; plots in notebooks)
     • Wiener Process
     • Geometric Brownian Motion
     • Euler-Maruyama Method for Stochastic Differential Equations (SDE)
     • Price of a Perpetual Put Option

4. Conclusion

   • Summary and Outlook

5. Literature

   • Main Literature: A Game-Theoretic Analysis of Options
   • Supplementary Texts: Game Theory Models, Numerical Methods, and Applications
   • Lecture Notes: Mathematical Modeling and Simulation
   • Lecture Notes: Derivatives