Module Overview

Financial Mathematics II

This module introduces the learner to the mathematics of hedging and pricing of financial derivatives by arbitrage in a continuous-time framework by building on prior knowledge of discrete-time models. Key concepts such as conditional expectation, martingales, change-of-measure, Wiener processes, and Ito calculus are developed in the lead up to the derivation of the Black-Scholes formula and Black-Scholes equation. Monte Carlo methods are considered for solving stochastic differential equations.

Module Code

MATH 4818

ECTS Credits


*Curricular information is subject to change

Brownian motion

Transition from discrete to continuous processes, properties of Brownian motions


Stochastic calculus

Non-stochastic calculus, stochastic integration and differentials, Ito's Lemma, Ito calculus


Change of measure

Girsanov’s theorem, martingale representation theorem


Black Scholes formula and equation

Derivation, pricing, manipulation


Monte-Carlo methods for option pricing

Euler scheme, Milstein scheme, convergence


Lectures supported by problem-solving sessions and the use of mathematical software packages where applicable.

Module Content & Assessment
Assessment Breakdown %
Formal Examination100