Teaching Statistics in Finance
The course gives an overview of what might be taught in a third year ‘Statistics in Finance’ course based at medium second year mathematical and statistical levels. Financial background is not assumed and the topics treated begin with ideas of interest and the present and future values of money in financial legislation and everyday use. Financial return is considered for investments such as stocks and bonds. A major part of the course is concerned with developing the statistical fundamentals of investment diversification, the balancing of expected return and risk, though a mathematically satisfying development of mean and variance portfolio theory; it is applied with stock market data. The topic involves studying linear combinations of dependent investment returns as random variables and naturally motivates the introduction of financial concepts such as short selling, holding long, capital allocation and efficient frontiers. Optimal efficient frontier portfolios, according to different ways of balancing expected return and risk over pre-chosen sets of individual investments, are derived by employing Lagrange functions and numerical optimization. Simple expositions of options and arbitrage are suggested, with more detail including Black-Scholes pricing of options being given in the comprehensive set of notes associated with the course. Illustrations with fragments of Maple and Matlab software and their output are also included, and indicate their use in student exercises. Student appreciation appears to derive from seeing the interesting and practical application of previously studied statistical topics. Lecturers may appreciate the mathematical and statistical perceptions arising in development of the financial topics, more so than in customary settings.
The course has evolved from preceding years of somewhat experimental undergraduate teaching in the area. It has been presented to mixed audiences of academics and professionals at Queensland University of Technology as part of a continuing education programme, and twice under the LTSN’s Day-break programme. Encouraging feed-back was received from these presentations. The material is scheduled for future book publication.
Statistical Analysis and Modelling of Financial Time Series
This course is concerned with the statistical theory and practice of financial time series modelling and forecasting. It is in three parts. Part 1 covers exploratory statistical methods for various features, such as trend, drift, seasonality, linear and non-linear dependence, short and long memory, dependence, directionality, volatility and volatility-dependence. Part 2 is concerned mostly with traditional linear modelling. Part 3 presents nonlinear models in a mathematically accessible manner, firstly just involving volatility, and then with extensions incorporating local behaviour in both level and volatility. Explicit results for nonlinear models mean that they are treated in parallel detail to those for linear models. Illustrations throughout use stock prices, index series, interest rate series and exchange rate series, and guidance on the use of easily availble packages is included.