Mathematical Finance in Continuous Time - MAT00097H
Module summary
Module gives an introduction to classical methods of asset pricing in continuous time.
Professional requirements
Counts towards IFoA exemption.
Related modules
Pre-requisite modules
Module will run
| Occurrence | Teaching period |
|---|---|
| A | Semester 2 2025-26 |
Module aims
The module introduces and applies the main mathematical continuous-time tools that are used to value assets that are traded in financial markets, such as bonds, futures and options.
Module learning outcomes
After successful completion of this module, students are able to
apply and explain:
• some basic concepts and results of
stochastic calculus in continuous time;
• the
Black-Scholes formula for option pricing;
• basic models
of interest rates;
• basic credit risk models.
Module content
• Stochastic Processes in continuous time.
•
Stochastic calculus.
• Black-Scholes model of a stock
market.
• Black-Scholes pricing formula for European call
options.
• Pricing of credit risk instruments.
•
Pricing of fixed-income securities.
Indicative assessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 80.0 |
| Essay/coursework | 20.0 |
Special assessment rules
None
Indicative reassessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 80.0 |
| Essay/coursework | 20.0 |
Module feedback
Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
Indicative reading
Z. Brzezniak, T. Zastawniak, Basic stochastic processes : a course through exercises. Springer
M. Capinski and T. Zastawniak, Mathematics for Finance. An Introduction to Financial Engineering, Springer
M. Capinski and T. Zastawniak, Credit Risk (elect. resource)
D. McInerney and T. Zastawniak, Stochastic Interest rates (elect. resource)
M. Musiela, M. Rutkowski, Martingale Methods in Financial Modelling, Springer.
M. Steele, Stochastic calculus and financial applications, Springer