2003/2004 Semester 1

**Lecturer:** Dr Chan Yiu Man

Office: S16, #07-110

Tel: 68742950

Email: stacym@nus.edu.sg

**Lectures: **Friday 6:45pm to 9:45pm at Lab 15 (1/8, 8/8, 15/8, 22/8, 29/8)

**Tutorial: **Friday 6:45pm to 9:45pm at Lab 15 (5/9)

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**Course Objectives**

Part I of the module introduces key ideas in calculus and algebra, as well as concepts in probability, statistics, and time series. It serves to introduce students to various quantitative methods that can be used in finance.

**Reading materials**

As the topics are very broad, so no single textbook will be adequate for this module. It is appreciated that students come from various backgrounds. For some students they may not require readings on certain topics. The list below is thus complied only as a guideline, and is aimed at supplementing the lecture notes.

Watsham T and Parramore K, * Quantitative Methods in Finance*, 1997, International Thomson Business Press, Call# HF5691 Wat (

Levine D M, Stephan D, Krehbiel T C & Berenson M L, * Statistics for Managers Using Microsoft Excel*, 3

Chiang, A.C., * Fundamental Methods of Mathematical Economics*, 3

Hanke, H.E., and A.G. Reitsch, * Business Forecasting*, 6

** FE 5102 Quantitative Methods and Programming **

** Part I**: Basic probability concepts and statistical distributions. Concepts of calculus and algebra and their applications in finance. Time series and measures of trends and volatilities. Use of statistical software in computations, estimation, inference, and simulations.

** Topics:**

** 1) Algebra and Calculus **

Exponents and logarithms, arithmetic and geometric progressions, matrix algebra, quadratic forms, positive-definite and negative-definite matrices, differential calculus, some rules of differentiation, monotonic, concave and convex functions, optimization, Taylor’s series expansion, multivariate function, partial derivative, optimization of bivariate function, gradient and Hessian matrix, optimization of multivariate functions, constrained optimization, integral calculus, definite and indefinite integrals. (**WP**: Ch 3, **C**: 4.1, 4.2, 4.3, 4.5, 4.6, 6.2, 6.3, 7.1, 7.2, 7.3, 7.4, 10.1, 10.3, 10.4, 10.5, 13.2, 13.3)

** 2) Fundamentals of Probability and Statistics **

Probability laws, distribution laws, density function and cumulative distribution function, expectation, descriptive statistics, bivariate distributions, correlation coefficients, conditional density and expectation, Central Limit Theorem, some special distributions: binomial, Poisson, normal and lognormal, lognormal distribution and the continuously compounded rate of return. (**WP**: Ch 4, **LSKB**: Ch 4, 5)

** 3) Statistical methods **

Statistical estimation, statistical inference, hypothesis testing, p-value and level of significance, confidence and forecast interval, regression analysis, estimation of linear regression model, nonlinear regression, time-series regression, nonparametric methods. (**WP:** Ch 5, 6, **LSKB**: Ch 6, 7, 8, 9, 10, 11, 12, **HR:** Ch 6, 7)

** 4) Time series analysis **

Nature of time series, stationarity versus nonstationarity, autoregressive moving average (ARMA) processes, autocorrelation, partial autocorrelation function, portmanteau statistics, unit-root test, financial time series models: random walk, martingale, mean-reversion processes, long memory processes, models with conditional heteroscedasticity, GARCH, EGARCH and TARCH models, asymmetry in conditional volatility: the leverage effect, a case study of the Straits Times Index. (**WP:** Ch 7, **LSKB:** Ch 13, **HR:** Ch 5, 8, 10)

To send the lecturer an email, click <stacym@nus.edu.sg>

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Last modified: 21 July 2003.