Postgraduate / Master's · Advanced Mathematics
Stochastic Calculus
What is it
Stochastic calculus extends ordinary calculus to functions influenced by randomness, most notably through Brownian motion and Itô's lemma — a specialised chain rule needed because random processes aren't differentiable in the usual sense.
Why it matters
Stochastic calculus is the mathematical foundation of modern quantitative finance — options pricing models like Black-Scholes are derived directly from stochastic calculus, making this essential for anyone pursuing research or careers in financial mathematics.
Exam tip
Remember that Itô's lemma includes an extra second-derivative term that ordinary calculus's chain rule doesn't have — forgetting this term is the single most common error when first applying stochastic calculus, and it's precisely what makes it different from ordinary calculus.
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