Mathematical Finance

MAT 4051

This course introduces the Black-Scholes model – a model which is the backbone of derivatives trading, a multitrillion-dollar industry. In answering the financial question, “What is the fair price of an option?” we will have to introduce a rather involved mathematical machinery. The BS model is founded on two important assumptions: the principle of no-arbitrage and the assumption that prices follow a random-walk/Brownian motion, i.e., that prices satisfy a diffusion equation. We begin with the conceptually simpler discrete time approach (binary trees) and time permitting we extend to continuous time (Brownian motion, stochastic differential equations – the Black-Scholes equation, stochastic integration). Much of the mathematics of BSM is based on probability theory. No prior knowledge of finance is necessary.

Credits: 3 Cr.