Introduction

Having existed separately for hundreds of years, the fields of finance and physics have become inextricably linked in the last century. Key in the development of financial physics was the invention and success of the Black-Scholes model, a method for formalising the pricing of options. It utilises the mathematics of stochastic processes which are used to describe physical phenomena, principally Brownian motion. The Black-Scholes formula prompted a boom in the options market, used to great effect by companies such as LTCM. However, limitations of the model caused many of the institutions applying the Black-Scholes equation to ultimately fail, often due to shocks in the market that the model cannot account for. The successes and failures of the Black-Scholes model raise important questions regarding the effectiveness of modelling financial markets using physical models, and the responsibility of physicists and mathematicians becoming involved in financial markets and financial policy development.

We must first understand the Black-Scholes model’s mathematical and physical foundations. In the Black-Scholes model the value of an asset, be it a stock, bond or house, is modelled using a stochastic process called geometric Brownian motion. In this website, we will discuss:  

  • What is meant by a stochastic process. 
  • Understand the properties of geometric Brownian motion and its importance in finance. 
  • The historical advancements in modelling financial systems as Brownian motion and finally derive the Black-Scholes equation.  
  • The real-world applications of the Black-Scholes model and its limitations. 
  • A case study: the rise and fall of the hedge fund founded by the developers of the Black-Scholes model and the lessons from its collapse. 
  • How the limitations of the Black-Scholes are addressed: are physics principles truly applicable in a financial framework. 

To fully engage with this project requires a basic understanding of differential equations and calculus. As a result, this project is aimed towards students who have completed their first year of an undergraduate physics degree. However, the content of this project will be of interest to a broader audience, even if they do not grasp some of the mathematical ideas involved.