Preface

In this course, you will learn, define, and apply various relevant probability concepts to quantitative finance, such as:

• Basic Probability Theory and Set Operations
• Combinatorial Analysis
• Conditional Probability
• Bayes Theorem
• Distributions - Discrete and Continuous
• Expected Value Theory
• Covariance and Correlation
• Bonus: Markov Chains

In the early 20th century, French mathematician Louis Bachelier introduced a revolutionary idea in his seminal paper, "The Theory of Speculation," where he suggested that stock prices follow a 'random walk' governed by probability theory. According to Bachelier, stock prices exhibit randomness and are best described by a normal distribution, with each price movement being independent of previous ones. This probabilistic approach to price behavior laid the groundwork for future financial models. The concept gained further validation in 1973 with the Black-Scholes model developed by Fischer Black, Myron Scholes, and Robert Merton, which formalized the use of probability in pricing derivatives. Their model, which assumes stock prices follow a normal distribution with a steady upward drift, has become a cornerstone in the realm of quantitative finance.

The success of these probabilistic models has cemented the role of probability theory in quantitative finance, making it a central topic in interviews for finance interns and graduates.