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For Prospective Students

Financial Mathematics Program

Introduction

Research in Financial Mathematics is obviously interdisciplinary, but it primarily hinges on sophisticated mathematical tools such as: theory of probability, theory of martingales, Ito's stochastic calculus, stochastic differential equations, stochastic backward differential equations, partial differential equations, variational inequalities, optimisation methods, stochastic optimal stopping, stochastic optimal control, Dynkin's games, stochastic differential games, statistics of stochastic processes and, last but not least, various computational methods used in financial applications.

The School offers a variety of specialised units of study in the broad area of Financial Mathematics and Statistics, which cover most of the abovementioned areas of mathematical knowledge and range from introductory units for undergraduates to advanced units for honours students. We thus give you an opportunity to complete high-quality BSc/honours/masters teaching programs capable of competing with analogous programs at other universities in Australia. The BSc and BSc (Advanced) degrees allow you to major in Financial Mathematics and Statistics; for more details, see here.

The best graduates with specifically strong mathematical and statistics backgrounds are in very high demand by the finance industry in Australia and worldwide. In particular, they can seek employment as risk managers or quantitative analysts (quants) in the following roles:

  • front office/desk quants who work on implementation of pricing and hedging models directly used by traders,
  • model validating quants who independently implement pricing models in order to validate models used by the front office models,
  • research quants whose task is to invent and develop new pricing approaches and original models for new financial products,
  • capital quants who work on modelling the bank’s credit exposures and capital requirements imposed by a regulatory agency (such as APRA),
  • quant developers who take care of computer programs for implementation of pricing models,
  • statistical arbitrage quants who work on finding patterns in market data to support HFT (high-frequency trading) automated trading platform.

Prospective employers of graduates in Financial Mathematics and Statistics can be roughly classified as follows:

  • major retail banks, such as: CBA, NAB, ANZ, Westpac, Bank of Queensland, ...
  • investment banks, such as: Macquarie Group, UBS, Credit Suisse, Goldman Sachs, HSBC, ...
  • hedge funds, such as: K2 Asset Management, Platinum Asset Management, ...
  • wealth management companies, such as: AMP, Vanguard Investment, Russell Investments, ...
  • proprietary trading firms, such as: Optiver Asia Pacific, Propex Derivatives, Lepus, ...
  • accountancy firms, such as: PricewaterhouseCoopers (PwC), Ernst and Young, Deloitte, KPMG, ...
  • consulting firms, such as: Accenture, Ernst and Young, Deloitte Consulting, PwC, ...
  • insurance companies and superannuation funds,
  • as well as software companies.

The School's coordinator for the Financial Mathematics and Statistics programs is Prof Marek Rutkowski. For further information, you may also contact Dr Anna Aksamit, Prof Ben Goldys, Dr Ray Kawai or Dr Zhou Zhou.

Currently Available Financial Mathematics Units

The following undergraduate and honours units of study are available in 2019. New 4000-level units in Stochastic Analysis and Financial Mathematics will be offered from 2020 (Bachelor of Advanced Studies program).

MATH2070/2970 Optimisation and Financial Mathematics

The first part of this intermediate unit looks at programming problems and their solution using the simplex algorithm, nonlinear optimisation and the Karush-Kuhn-Tucker conditions. The second part includes an introduction to some problems and techniques from Financial Mathematics, such as: the pricing of riskless and risky securities, the modern portfolio theory (MPT) due to H. Markowitz, the capital asset pricing model (CAPM), and the dynamic programming principle (DPP) due to R. Bellman. The unit is offered at both advanced and standard levels. The prerequisites for Optimisation and Financial Mathematics are junior mathematics units (taken at either standard or advanced level) covering differential calculus, linear algebra, integral calculus & modelling and statistics.

MATH3075/3975 Financial Derivatives

This senior year unit focuses on arbitrage-free pricing of modern financial derivatives, such as equity options of either a European or an American style. The theory of arbitrage-free pricing is underpinned by the concept of hedging through dynamic trading in primary securities. The main mathematical tools taught in this unit are: the theory of discrete-time martingales originated by J. L. Doob, an equivalent change of a probability measure technique (the Radon-Nikodym density), which leads to the risk-neutral valuation formula, and solution to the optimal stopping problem through the backward induction. The unit covers discrete-time models, such as the Cox-Ross-Rubinstein binomial model of the stock price, as well as the celebrated continuous-time Black-Scholes model based on the Wiener process. This unit is offered at both advanced and standard levels.

FMAT3888 Projects in Financial Mathematics

Mathematics and Statistics are powerful tools in finance and, more generally, in the world at large. To really experience the power of mathematics and statistics at work, students need to identify and explore interdisciplinary links. Engagement with other disciplines also provides essential foundational skills for using mathematical and statistical ideas in financial contexts and in the world beyond. In this unit you will commence by working on a group project in an area of Financial Mathematics or Statistics. From this project you will acquire skills of teamwork, research, writing and project management as well as disciplinary knowledge. You will then have the opportunity to apply your disciplinary knowledge in an interdisciplinary team to identify and solve problems and communicate your findings.

MSH Introduction to Stochastic Calculus with Applications

This Statistics honours unit explores some fundamental concepts and results from the Ito stochastic calculus, such as: conditional expectations, filtrations, martingales, stopping times, the Wiener process (Brownian motion), the Ito stochastic integral, semimartingales, Ito's lemma, Levy's characterization theorem, martingale representation property, stochastic differential equations and stochastic exponentials, Feynman-Kac formula, Girsanov's theorem, and distributions of first passage times for the Wiener process. It is essential that students have a very good command of the contents of STAT2911 (Probability and Statistical Models) and STAT3021/3911 (Stochastic Processes).

AMH Advanced Option Pricing

This Applied Mathematics honours unit is an advanced program designed for top students and includes the latest mathematical techniques for pricing derivative securities and exotic options in continuous-time models for equities and foreign exchange. A detailed study of the problem of pricing and exercising of an American put option in the Black-Scholes model is provided. A substantial part of the unit is devoted to generalizations of the classical Black-Scholes model, such as: the constant elasticity of variance (CEV) model, the local volatility model due to B. Dupire, modelling of stochastic volatility (in particular, the Heston model) and the issue of model risk (in particular, the robustness of the Black-Scholes model). This unit is available to fourth year (Honours) students and it requires the working knowledge of the Ito stochastic calculus, which is taught in Statistics honours unit ''Introduction to Stochastic Calculus with Applications.''

BSc Major in Financial Mathematics and Statistics

Students in the BSc and BSc (Advanced) degrees can choose to major in Financial Mathematics and Statistics.

By choosing the core units of study and one of the electives from the lists below, you will graduate with a major in Financial Mathematics and Statistics. Most of the core and elective units are offered at two levels (mainstream and advanced) right through from first year to the end of third year. You may also elect to have your major area of study printed on your testamur, identifying your expertise in financial mathematics and statistics to prospective employers.

BSc (Honours) in 2019. The best students who complete a major in Financial Mathematics and Statistics in 2018 may also consider completing a fourth (Honours) year in 2019 by combining Introduction to Stochastic Calculus with Applications and Advanced Option Pricing with other fourth year units drawn from Mathematics and Statistics and writing an essay/project in Financial Mathematics (for more details, see the handbook for Honours in Applied Mathematics AMH).

Bachelor of Advanced Studies in 2020. The best students who complete a major in Financial Mathematics and Statistics in 2019 may go on to Bachelor of Advanced Studies (either with or without honours) in Financial Mathematics and Statistics in 2020 (new fourth-year teaching program to be offered in 2020).

Units of Study for a Major in Financial Mathematics and Statistics in 2019 (new curriculum)

For the new requirements for completion of Financial Mathematics and Statistics major, please refer to the handbook FMS Major.

Core Junior units (12 cp)

  • MATH1002/1902 Linear Algebra (3cp, Sem 1)
  • MATH1021 Calculus of One Variable (3cp, Sem 1 + Sem 2)
  • MATH1921/1931 Calculus of One Variable (3cp, Sem 1)
  • MATH1023 Multivariable Calculus and Modelling (3cp, Sem 1 + Sem 2)
  • MATH1923/1933 Multivariable Calculus and Modelling (3cp, Sem 2)
  • MATH1005 Statistical Thinking with Data (3cp, Sem 1 + Sem 2)
  • MATH1905 Statistical Thinking with Data (3cp, Sem 2)
  • DATA1001/1901 Foundations of Data Science (6cp, Sem 1 + Sem 2)
    (Note that either MATH1005/1905 or DATA1001 should be completed.)

Core Intermediate units (12 cp)

  • STAT2011/2911 Probability and Estimation Theory/Probability and Statistical Models (6cp, Sem 1)
  • MATH2070/2970 Optimisation and Financial Mathematics (6cp, Sem 2)

Core Senior units (12 cp)

  • MATH3075/3975 Financial Derivatives (6cp, Sem 2)
  • FMAT3888 Projects in Financial Mathematics (6cp, Sem 2)
  • SCPU3001 Science Interdisciplinary Project (6cp, Sem1 + Sem 2)
    (Note that either FMAT3888 or SCPU3001 should be completed.)

Senior elective units in Mathematics (at least one must be taken)

  • MATH3076 Mathematical Computing (6cp, Sem 1)
  • MATH3979 Complex Analysis (6cp, Sem 1)
  • MATH4071 Convex Analysis and Optimal Control (6cp, Sem 1)
  • MATH4076 Computational Mathematics (6cp, Sem 1)

Senior elective units in Statistics (at least one must be taken)

  • STAT3021 Stochastic Processes (6cp, Sem 1)
  • STAT3022/3922 Applied Linear Models (6cp, Sem 1)
  • STAT3023/3923 Statistical Inference (6cp, Sem 1)

Units of Study for a Major in Financial Mathematics and Statistics in 2019 (old curriculum)

The following list of units refers to the old requirements for completion of Financial Mathematics and Statistics major.

x Core Junior units

  • MATH1001/1901/1906 Differential Calculus
  • MATH1002/1902 Linear Algebra
  • MATH1003/1903/1907 Integral Calculus and Modelling
  • MATH1005/1905 Statistics

x Core Intermediate units

  • MATH2070/2970 Optimisation and Financial Mathematics
    (Note that one further MATH 2xxx unit is required, in order to meet the prerequisites for the senior core unit MATH 3075/3975.)
  • STAT2011/2911 Statistical Models
  • STAT2012/2912 Statistical Tests

Core Senior units (18cp)

  • STAT3021 Stochastic Processes (6cp, Sem 1)
  • STAT3022/3922 Applied Linear Models (6cp, Sem 1)
  • MATH3075/3975 Financial Derivatives (6cp, Sem 2)

Senior elective units (at least one must be taken)

  • MATH3971 Convex Analysis and Optimal Control (6cp, Sem 1)
  • MATH3076/3976 Mathematical Computing (6cp, Sem 1)
  • MATH3974 Fluid Dynamics (6cp, Sem 1)
  • FMAT3888 Projects in Financial Mathematics (6cp, Sem 2)
  • MATH3969 Measure Theory and Fourier Analysis (6cp, Sem 2)
  • MATH3078/3978 PDEs and Waves (6cp, Sem 2)
  • STAT3023/3923 Statistical Inference (6cp, Sem 1)
  • STAT3888 Statistical Machine Learning (6cp, Sem 2)
  • DATA3404 Data Science Platforms (6cp, Sem 1)

Most of the Mathematics and Statistics units of study mentioned above have their own web pages.
Core units: MATH1002, MATH1902, MATH1021, MATH1921, MATH1931, MATH1923, MATH1933, MATH1005, MATH1905, DATA1001, DATA1901, MATH2070, MATH2970, STAT2011, STAT2911, MATH3075, MATH3975, FMAT3888.
Electives: MATH3971, MATH3076, MATH3976, MATH3078, MATH3978, MATH3969, MATH3974, STAT3021, STAT3911, STAT3022, STAT3922, STAT3023, STAT3923, STAT3888, DATA3404.