Module manager: Dr Khoa Le
Email: K.Le@leeds.ac.uk
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2026/27
None
| MATH5320M | Discrete Time Finance |
This module is not approved as an Elective
This module introduces students to the mathematical foundations and financial applications of continuous-time models in finance. It focuses on the use of stochastic calculus to model asset prices and derive key results in modern financial theory. Students will explore the behaviour of financial markets through continuous-time stochastic processes and learn how these models underpin derivative pricing and risk management.
Through a rigorous yet practical approach, the module covers the formulation and interpretation of stochastic differential equations, the application of Ito’s Lemma, and the derivation of the Black-Scholes formula. It also explores the principles of arbitrage, state pricing, and the concept of equivalent martingale measures, providing a comprehensive framework for understanding the pricing of financial securities in a dynamic market environment.
Students learn mathematical concepts through lectures and apply them to practice problems during workshops.
Subject specific learning outcomes:
On completion of this module, students will be able to:
1. demonstrate a familiarity with continuous-time stochastic processes,
2. interpret a stochastic differential equation and its solution
3. explain and apply the log-normal asset pricing model
4. apply Ito's formula
5. derive the Black-Scholes formula
6. explain the arbitrage principle and its application to securities pricing
7. explain state prices and the concept of equivalent martingale measures
Skills learning outcomes:
On successful completion of the module students will be able to:
Manage time effectively and work independently to meet deadlines.
Apply analytical thinking and technical knowledge to solve problems in financial mathematics and interpret results.
Communicate mathematical and financial concepts clearly in multiple formats.
Critically evaluate financial models, assessing their assumptions, limitations, and practical implications.
Self-financing portfolio and arbitrage
Stochastic processes and stochastic calculus with respect to Brownian motion
Continuous-time models (Black-Scholes model, Heston model)
Risk-neutral measures and change of measures
Option pricing and replication
Additional topics that build on these may be covered as time allows. Such topics may be drawn from the following, or similar: Interest rate modelling, American and exotic options, Greeks
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 22 | 1 | 22 |
| Practical | 11 | 1 | 11 |
| Private study hours | 117 | ||
| Total Contact hours | 33 | ||
| Total hours (100hr per 10 credits) | 150 | ||
117
Feedback on problem sheets will be provided orally to students during lectures/practicals. Individual feedback will be provided during office hours as required.
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Standard exam (closed essays, MCQs etc) (S1) | 3.0 Hrs 0 Mins | 100 |
| Total percentage (Assessment Exams) | 100 | |
The assessment details for this module will be provided at the start of the academic year
Check the module area in Minerva for your reading list
Last updated: 30/04/2026
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