# Postgraduate Courses

- MAFS 5010Stochastic Calculus[3-0-0:3]Previous Course Code(s)MAFS 501DescriptionRandom walk models. Filtration. Martingales. Brownian motions. Diffusion processes. Forward and backward Kolmogorov equations. Ito's calculus. Stochastic differential equations. Stochastic optimal control problems in finance.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Develop a rigorous probabilistic framework and lay a firm foundation for stochastic calculus.
- 2.Recognize the most important results, including Ito's Lemma, Girsanov change of measure.
- 3.Employ numerical PDE or Monte Carlo method to solve the stochastic differential equations.
- 4.Recognize the Black-Scholes models and more general diffusion models.
- 5.Apply the theory in stochastic calculus to financial problems, e.g. option pricing.

- MAFS 5020Advanced Probability and Statistics[3-0-0:3]Previous Course Code(s)MAFS 502BackgroundEntry PG level MATHDescriptionProbability spaces, measurable functions and distributions, conditional probability, conditional expectations, asymptotic theorems, stopping times, martingales, Markov chains, Brownian motion, sampling distributions, sufficiency, statistical decision theory, statistical inference, unbiased estimation, method of maximum likelihood.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Recognize fundamental concept of randomness and analyze it using probability framework.
- 2.Recognize the law of large numbers and the central limit theorem and their applications.
- 3.Evaluate the statistical procedure of data analysis.
- 4.Formulate the basic statistical problems from one sample problem to linear regression.
- 5.Apply methodology of statistical inference to solve practical problems.

- MAFS 5030Quantitative Modeling of Derivatives Securities[3-0-0:3]Previous Course Code(s)MAFS 503Exclusion(s)MATH 5510 (prior to 2018-19)BackgroundEntry PG level MATHDescriptionForward, futures contracts and options. Static and dynamical replication. Arbitrage pricing. Binomial option model. Brownian motion and Ito's calculus. Black-Scholes-Merton model. Risk neutral pricing and martingale pricing methodology. General stochastic asset-price dynamics. Monte Carlo methods. Exotic options and American options.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Formulate and evaluate pricing models for derivatives.
- 2.Analyze effectiveness of hedging strategies for monitoring risks in derivatives.
- 3.Make appraisal of the dynamics of stock prices and commodity prices.
- 4.Provide solution using structural derivatives in wealth management.

- MAFS 5040Quantitative Methods for Fixed-Income Instruments[3-0-0:3]Previous Course Code(s)MAFS 504Exclusion(s)MATH 5520BackgroundEntry PG level MATHDescriptionBonds and bond yields. Bond markets. Bond portfolio management. Fixed-income derivatives markets. Term structure models and Heath-Jarrow-Morton framework for arbitrage pricing. Short-rate models and lattice tree implementations. LIBOR Market models. Hedging. Bermudan swaptions and Monte Carlo methods. Convexity adjustments. Mortgage-backed securities. Asset-backed securities. Collateralized debt obligations.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Describe the operation of fixed-income markets and the roles of the fixed-income derivative.
- 2.Apply major mathematical tools for fixed-income modeling.
- 3.Formulate major classes of fixed-income models and apply them for fixed-income pricing and risk management.
- 4.Evaluate the effectiveness of popular models for different sectors of derivatives.
- 5.Analyze exotic derivatives and choose pricing models.

- MAFS 5110Advanced Data Analysis with Statistical Programming[3-0-0:3]Previous Course Code(s)MAFS 511DescriptionData analysis and implementation of statistical tools in a statistical program, like SAS, R, or Minitab. Topics: reading and describing data, categorical data and longitudinal data, correlation and regression, nonparametric comparisons, ANOVA, multiple regression, multivariate data analysis.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Identify and explain the core ideas on financial data analysis by using statistical models.
- 2.Apply rigorous, analytic, highly numerate approaches to analyze and solve problems in daily life and at work with SAS and R, especially in finance.
- 3.Carry out objective analysis and prediction of quantitative information in finance with independent judgment.
- 4.Communicate effectively about statistical results obtained from R and SAS to both lay and expert audiences utilizing appropriate information and suitable technology.

- MAFS 5130Quantitative Analysis of Financial Time Series[3-0-0:3]Previous Course Code(s)MAFS 513Co-list withMSBD 5006Exclusion(s)MSBD 5006, MSDM 5053BackgroundEntry PG level MATHDescriptionAnalysis of asset returns: autocorrelation, predictability and prediction. Volatility models: GARCH-type models, long range dependence. High frequency data analysis: transactions data, duration. Markov switching and threshold models. Multivariate time series: cointegration models and vector GARCH models.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Recognize market indexes, financial time series and their features.
- 2.Recognize the foundation of time series and basic time series models.
- 3.Formulate time series models to study financial data, including market returns and volatility.
- 4.Evaluate the relationships of different markets via the cointegration time series and ECM models.
- 5.Analyze the real financial data with the statistical techniques from this course via a course project.

- MAFS 5140Statistical Methods in Quantitative Finance[3-0-0:3]BackgroundUndergraduate level knowledge in probability and statisticsDescriptionThis course provides an introduction to statistical models used in financial data analysis. Students learn about various basic and advanced regression models, and techniques of data analysis. These statistical methods are applied in quantitative finance, including portfolio theory, asset pricing models and risk management.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Apply data analysis and statistical inference in financial applications.
- 2.Formulate the construction of the factor models and apply them in asset management and other applications.
- 3.Perform statistical analysis of investment models.
- 4.Analyze financial problems using the Bayesian methods and nonlinear regression models.
- 5.Evaluate the effectiveness of statistical trading strategies.
- 6.Design and evaluate statistical models of risk management and their implementation.

- MAFS 5210Mathematical Models of Investment[3-0-0:3]Previous Course Code(s)MAFS 521DescriptionUtility theory, stochastic dominance. Portfolio analysis: mean-variance approach, one-fund and two-fund theorems. Capital asset pricing models. Arbitrage pricing theory. Consumption-investment problems.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Apply investment models in financial applications.
- 2.Formulate quantitative investment with Mean-Variance Optimization and Black-Litterman models.
- 3.Analyze equity valuation using asset pricing models.
- 4.Evaluate the effectiveness of investment strategies.
- 5.Design and implement asset management strategies and structured solutions.

- MAFS 5220Quantitative and Statistical Risk Analysis[3-0-0:3]Previous Course Code(s)MAFS 522DescriptionVarious risk measures such as Value at Risk and Shortfall Risk. Coherent risk measures. Stress testing, model risk, spot and forward risk. Portfolio risks. Liabilities and reserves management. Case studies of major financial losses.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Analyze risk on derivatives and other financial products using quantitative and statistical methods.
- 2.Evaluate the price impact on financial products due to quantifiable risks.
- 3.Devise computer programs to compute the risk using numerical methods.
- 4.Analyze the capital requirements for financial institutions using quantitative and statistical methods.

- MAFS 5230Advanced Credit Risk Models[3-0-0:3]Previous Course Code(s)MAFS 523DescriptionCredit spreads and bond price-based pricing. Credit spread models. Recovery modeling. Intensity based models. Credit rating models. Firm value and share price-based models. Industrial codes: KMV and Credit Metrics. Default correlation: copula functions.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Describe credit markets and the roles of the fixed-income derivative.
- 2.Apply advanced mathematical tools for single-name and multiple-name credit derivatives modeling.
- 3.Identify risk factors of credit derivatives and formulate major classes of credit-risk models accordingly.
- 4.Evaluate the effectiveness of various models for different sectors of credit derivatives.
- 5.Implement various models through quantitative computing.

- MAFS 5240Software Development with C++ for Quantitative Finance[3-0-0:3]Previous Course Code(s)MAFS 524BackgroundPrior programming experienceDescriptionThis course introduces C++ with applications in derivative pricing. Contents include abstract data types; object creation, initialization, and toolkit for large-scale component programming; reusable components for path-dependent options under the Monte Carlo framework.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Design and develop functions in C++ for financial applications.
- 2.Recognize the basic object oriented modeling and programming paradigm and its application on computational finance.
- 3.Translate financial models into C++ applications.
- 4.Handle the complexities in real world financial calculations.

- MAFS 5250Computational Methods for Pricing Structured Products[3-0-0:3]Previous Course Code(s)MAFS 525BackgroundEntry PG level MATHDescriptionComputational methods for pricing structured (equity, fixed-income and hybrid) financial derivatives products. Lattice tree methods. Finite difference schemes. Forward shooting grid techniques. Monte Carlo simulation. Structured products analyzed include: Convertible securities; Equity-linked notes; Quanto currency swaps; Differential swaps; Credit derivatives products; Mortgage backed securities; Collateralized debt obligations; Volatility swaps.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Design computer algorithms for pricing structured derivatives.
- 2.Devise and compute hedging strategies for monitoring risks in derivatives.
- 3.Construct numerical algorithms for performing model calibration in pricing models of financial derivatives.
- 4.Provide solution using structural derivatives in wealth management.

- MAFS 5260Building Financial Applications with Java and VBA[3-0-0:3]Previous Course Code(s)MAFS 6010CBackgroundC++ Programming ExperienceDescriptionJava fundamentals include language syntax, classes and objects, inheritance, interface, polymorphism, exception handling. Object oriented programming and its application to computational finance. Basic skills on translating financial mathematics into spreadsheets using Microsoft Excel and VBA.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Design and develop programs in Java for financial application.
- 2.Work with large sophisticated software facilities.
- 3.Translate financial models into spreadsheet applications.
- 4.Use VBA to build user defined functions for computational finance.
- 5.Handle the complexities in real world financial calculations.

- MAFS 5270Mathematical Market Microstructure[3-0-0:3]Previous Course Code(s)MAFS 6010GDescriptionThis course will study special classes of stochastic processes that can capture market behavior at micro level and their practical implications in algorithmic and low-latency trading. Topics covered include structural models of price formation process at microstructure level, information-based vs. inventory-based models, stochastic control and optimization in trading, and real time risk management.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Apply mathematical theory of market microstructure in trading risk management.
- 2.Conduct data analysis with computer programming languages such as R and/or Python.
- 3.Analyze problems with real industry data (such as tick market data and trading data).
- 4.Draw meaningful implications to capture market behavior at micro level in algorithmic and low-latency trading.
- 5.Conduct independent research to handle the complexities in real-world trading applications.

- MAFS 6010Special Topics in Financial Mathematics[2-4 credits]Previous Course Code(s)MAFS 601BackgroundEntry PG level MATHDescriptionSelected special topics in Financial Mathematics of current interest but not covered by existing courses.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Identify and apply the theories and methods related to the course topic.
- 2.Recognize the major issues and updated development in the area of the course topic.
- 3.Relate the concepts and methodologies in the course topic to practical implementation in the financial industries.

- MAFS 6100Independent Project[3-6 credits]Previous Course Code(s)MAFS 610DescriptionCompletion of an independent project under the supervisor of a faculty in financial mathematics or statistics. Scope may include (i) identifying a non-reference problem and proposing the methods of solution, (ii) acquiring a specific research skill.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Critically analyze a selected topic to identify and formulate practical problems in financial mathematics.
- 2.Recognize the key issues analyzed in the models and their limitations.
- 3.Design effective analytical and computational solution methodologies to solve the formulated models.
- 4.Provide quantitative interpretations of various financial phenomena in the formulated problems from the numerical results.
- 5.Communicate solution concepts and methods effectively to a range of audiences, both orally and in writing.