MTH5510 - The mathematics of finance: From derivatives to risk - 2018

6 points, SCA Band 2, 0.125 EFTSL

Postgraduate - Unit

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.



Organisational Unit

School of Mathematical Sciences

Chief examiner(s)

Dr Hassan Fallahgoul


Dr Hassan Fallahgoul

Unit guides



  • Second semester 2018 (On-campus)


MTH3251 or MTH3260 or equivalent


Only students enrolled in the Master of Financial Mathematics can enrol in this unit. Exceptions can be made with permission from the unit co-ordinator.


Introduction to options. The binomial model. The Black-Scholes model. Partial differential equations. Black-Scholes formulae. American options. Exotic options.

Basic concepts of risk management. Multivariate models. Copulas and dependence. Aggregate risk. Extreme value theory. Credit risk models and insurance analytics.


On completion of this unit students will be able to:

  1. Develop specialised mathematical knowledge and skills within the fields of partial differential equations and probability theory.
  2. Understand the complex connections between specialised financial and mathematical concepts.
  3. Apply critical thinking to problems in partial differential equations that relate to financial derivatives.
  4. Apply critical thinking to problems in probability theory that relate to risk management.
  5. Apply problem solving skills within the finance context.
  6. Formulate expert solutions to practical financial problems using specialised cognitive and technical skills within the fields of partial differential equations and probability theory.
  7. Communicate complex information in an accessible format to a non-mathematical audience.


Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

Workload requirements

Two 2-hour lectures per week

See also Unit timetable information