MTH5210 - Stochastic calculus and mathematical finance - 2019

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

Chief examiner(s)

Professor Fima Klebaner

Coordinator(s)

Professor Fima Klebaner

Unit guides

Offered

Clayton

  • First semester 2019 (On-campus)

Prerequisites

MTH3251 or MTH3260 or equivalent

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.

Synopsis

Variations and quadratic variation of functions. Review of integration and probability. Brownian motion. Ito integrals and Ito's formula. Stochastic differential equations and diffusions. Calculation of expectations and PDE's, Feynman-Kac formula. Martingales and semimartingales. Change of probability measure and Girsanov theorem. Fundamental theorems of asset pricing. Change of numeraire. Application to options.

Outcomes

On completion of this unit students will be able to:

  1. Develop specialised mathematical knowledge and skills within the field of stochastic calculus.
  2. Understand the complex connections between financial and probabilistic concepts.
  3. Apply sophisticated stochastic modelling skills within the context of financial markets.
  4. Apply critical thinking to problems in stochastic calculus and financial mathematics.
  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 field of stochastic calculus.
  7. Communicate complex information in an accessible format to a non-mathematical audience.

Assessment

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 1.5-hour lectures and one 1-hour applied class per week

See also Unit timetable information