Module Overview

Financial Mathematics I

This module introduces the learner to the mathematics of pricing, construction and hedging of derivative securities. Discrete-time models form the foundation of our treatment with concepts such as change-of-measure and martingales introduced within this framework. Option pricing will be considered from the perspectives of replication and risk-neutral expectation. Parity relationships and binomial pricing methods will be explored for European and American options. Multi-step binomial models will be considered for standard and exotic options. A discrete treatment of Monte-Carlo methods to path-independent and path-dependent options will be considered.

Module Code

MATH 4807

ECTS Credits


*Curricular information is subject to change

Expected value versus arbitrage pricing

Expected value versus arbitrage pricing, time value of money


Binomial trees

Binomial model, derivative synthesis, replication, Arrow-Debreu securities, risk-neutral measure


Martingales, change-of-measure, representation

Stochastic processes, filtrations, claims, conditional expectation, martingales, binomial representation theorem


Binomial option pricing

Vanilla and exotic option pricing on multi-step binomial lattices, pricing inequalities


Discrete time Monte-Carlo pricing

Martingale measure pricing, confidence intervals for option prices


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

Module Content & Assessment
Assessment Breakdown %
Formal Examination100