units

MTH5530

Faculty of Science

18 September 2017 22 November 2024

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This unit entry is for students who completed this unit in 2016 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.

Monash University

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.

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Coordinator(s)

Dr Simon Clarke

Offered

Clayton

  • First semester 2016 (Day)

Synopsis

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.

Outcomes

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.

Assessment

Assignments: 10%
Minor project: 20%
Exam: 70%

Workload requirements

Two 1.5-hour lectures and one 1-hour tutorial per week

See also Unit timetable information

Chief examiner(s)

Associate Professor Gregoire Loeper

Co-requisites

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.