Itô's Lemma

Itô's Lemma is a fundamental tool in stochastic calculus that describes how a function of a random process (like a stock price modeled with randomness) evolves over time. It accounts for both the direct change in the process and the variability due to randomness. Essentially, it extends the usual chain rule to situations where the process involves unpredictable fluctuations, allowing us to accurately compute the change in a transformed variable when the underlying process is subject to continuous noise, such as in financial modeling and risk assessment.