MATH157 CM - Stochastic Calculus for Finance

This is an advanced course in Mathematical Finance. This course begins with the discussion of mathematical technology of filtrations, conditional expectations, martingales, and Markov processes. This will bring us to more advanced topics such as Brownian motion, stochastic integration, and Ito’s formula from stochastic calculus. Quantitative Finance part of this course will include pricing of European and American options, Fundamental Theorems of Asset Pricing, and term structure modeling, including the Heath-Jarrow-Morton model. We will develop the Black-Scholes option pricing formula and the Black-Scholes partial differential equation. Additional topics may include models of credit risk, simulation, and expected utility maximization.

Prerequisites: MATH 109 CM; and MATH 151 CM or MATH 131 CM

Offered: Occasionally

Credit: 1

Course Number: MATH157 CM