Stochastic calculus is the extension of regular calculus to processes that are everywhere continuous, but nowhere differentiable. This is important in modern finance because any market observable (such as a stock price, an interest rate, or the price of oil) will follow such a process. The central concepts in stochastic calculus are Brownian motion and 'quadratic variation'. From these two concepts, an entire new field of calculus arose, with an entirely new set of rules and notations built upon the framework of Lesbegue integration. I will go through these fundamental concepts and arrive at the celebrated Black Scholes equation that governs the price of a stock option.
Dr. Tom Davis received his undergrad in physics at the University of Guelph, PhD at the University of British Columbia working with Dr. Marcel Franz in the field of theoretical condensed matter physics. His thesis was titled "Macroscopic Quantum Phenomena: Cold Atomic Gases and High Temperature Superconductivity". After graduating, Tom started a career in quantitative finance at FINCAD and Numerix - companies that sell derivative analytics libraries to financial professionals. Five years ago, Tom moved to New York City to join FactSet, a financial data company. There, Tom has been instrumental in increasing the quality and coverage of fixed income analytics and growing the research team from 3 to over 40 people.