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.
- First semester 2019 (On-campus)
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 computational methods in finance. Partial differential equations. Numerical solutions of partial differential equations using finite-difference techniques, and the pricing of European options. Implicit, explicit and Crank-Nicolson schemes. Convergence and stability. Numerical solutions of free-boundary value problems and the pricing of American options. The Black-Scholes and Heston stochastic volatility models. Risk-neutral valuation. Tree methods. Introduction to Monte Carlo methods. Euler and Milstein discretization schemes. Variance reduction techniques. Monte Carlo methods for multi-dimensional problems.
On completion of this unit students will be able to:
- Develop specialised mathematical knowledge and computational skills within the fields of partial differential equations and probability theory.
- Understand the complex connections between specialised financial and mathematical concepts.
- Apply critical thinking to problems in partial differential equations that relate to financial derivatives.
- Apply computational problem solving skills within the finance context.
- Formulate expert solutions to practical financial problems using specialised cognitive and technical skills within the fields of partial differential equations and probability theory.
- 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.
Two 1.5-hour lectures and one 1-hour applied class per week
See also Unit timetable information