MTH5530 - Computational methods in finance - 2018

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:

1. Develop specialised mathematical knowledge and computational 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 computational problem solving skills within the finance context.
5. Formulate expert solutions to practical financial problems using specialised cognitive and technical skills within the fields of partial differential equations and probability theory.
6. 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 tutorial per week

See also Unit timetable information