Itô's lemma, also known as the Itô-Doeblin Formula, is a fundamental result in
stochastic calculus. It provides a rule for differentiating stochastic processes involving
Brownian motion. Named after the Japanese mathematician Kiyoshi Itô, this lemma plays a
central role in the development of stochastic calculus and its applications in quantitative
finance. It is extensively used in mathematical finance for pricing and risk management of
derivative securities. It allows for the derivation of stochastic differential equations and
facilitates the calculation of various quantities, such as option prices, implied volatilities, and
hedging strategies, through the application of stochastic calculus.