Mathematics and Finance, Part I: Historical Context | by Shafqat Shadaab | Jan, 2024
This is part one of three articles I have planned exploring the confluence of mathematics and finance. This article will focus on the history, covering the foundations of probabilistic models and option pricing in finance. Part II will expand on the usage of calculus and statistics. Lastly, Part III will be about the mathematical arsenal utilized by market makers & analysts; it will tie everything into the current state of the markets.
The marriage of mathematics and finance is not a modern phenomenon. Its roots can be traced back to the 17th century with the pioneering work of mathematicians like Blaise Pascal and Pierre de Fermat, who laid the groundwork for probability theory.
These two mathematicians, in the 1600s, engaged in a correspondence that is now considered seminal in the development of probability theory. Their discussions revolved around problems related to gambling and games of chance, which prompted the formalization of concepts in probability. This was crucial because the notions of risk and uncertainty are central to both gambling and financial decision-making.
As such, probability theory was initially used to analyze games of chance and solve problems related to gambling. Its potential for broader applications, such as in finance, began to be recognized only over time. The ability to quantify risk and make predictions based on probabilistic models became increasingly important in financial decision-making.
It was not until the 20th century that the full potential of mathematics in finance began to be realized.
Louis Bachelier’s 1900 doctoral thesis, titled “Théorie de la spéculation” (The Theory of Speculation), marks a pivotal moment in the application of mathematical concepts to finance, particularly the stock market. Bachelier, a French mathematician, was arguably the first person to model the stochastic process of stock market prices, an endeavor that laid the groundwork for what would eventually become the modern field of financial mathematics.
The key aspects covered in his thesis are-
- Random Walk Hypothesis: Bachelier’s most significant contribution was his conceptualization of stock price movements as a continuous stochastic process, which he termed “random…
