Degree Requirements

Random 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.

Probability 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. Background: Entry PG level MATH

Forward, 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.

Bonds 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.

This course covers advanced statistical approaches to analyze financial data with two open-source statistical and financial packages Python and R. The key topics of the course are: 1) Data mining to study how to read and describe financial data appropriately with Python and R; 2) Simple and Multiple linear regression modeling to capture the relationship between variables and do forecasting (e.g, how the change in the corporate AAA bond yield is related with the change in the 10-year Treasury bond rate, check the validity of CAPM, and some extensions of CAPM like Fama-French three factor model); 3) Analysis of variance (ANOVA) to compare the performance of different stock mutual funds and analyze whether or not different groups of corporate executives would yield different cash compensation; 4) Machine learning including logistic regression, SVM, decision tree, random forest, etc, and more financial and statistical models like generalized linear models, times series model and quantile regression models.

Analysis 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. Background: Entry PG level MATH

Description statistics and exploratory analysis. Basics of statistical inference. Linear regression. Principal components. Factor models. Statistical analysis of portfolio theory. CAPM and multifactor pricing models. Bayesian methods. Nonparametric regredss: Kernel smoothing. Projection pursuit and nerual nets. Boosting. Other nonlinear regression models. Statistical terading strategies. Statistical methods in risk management.

Utility theory, stochastic dominance. Portfolio analysis: mean-variance approach, one-fund and two-fund theorems. Capital asset pricing models.  Arbitrage pricing theory. Consumption-investment problems.

Nature of risk and risk measures. Reduced form models including Hazard rates and calibration, Exponential models of defaults and Contagion models. Mixture models including Bernoulli mixture models and CreditRisk+ models. Structural models including Merton model and mKMV, CreditMetrics and Gaussian copula, Vasicek model and Hull-White model. Credit derivatives and counter party risks.

This 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. Background: Prior programming experience

Computational 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. Background: Entry PG level MATH.

Previous Course Code(s): MAFS 6010G

This 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.

Previous Course Code(s): MAFS 6010L

The financial reforms in China have offered vast opportunities for companies to tap the onshore and offshore markets in financing, investment and risk management. This course introduces cross-border channels, structure products, and other emerging mechanisms for fund raising and risk hedging in Hong Kong and China. It also covers analyses of market players and the impacts on capital raising, investment strategies and FX hedging. Relevant current events and landmark deals are examined to illustrate teaching points.

Previous Course Code(s): MAFS 6010R

This course will explore the Markowitz portfolio optimization in its many variations and extensions, with special emphasis on R programming. Each week will be devoted to a specific topic, during which the theory will be first presented, followed by an exposition of a practical implementation based on R programming.

Previous Course Code(s): MAFS 6010N

Structured solutions including payoff design / packaging / distribution / pricing / hedging / funding; The popular structures in practice across the asset classes (Equity, Funds, FX, Interest Rate, Credit and Commodities); The customized index business based on factors, portfolio theory and other trading models with up-to-date industry practices; Computational methods for derivatives and structured products, including lattice tree methods, finite difference approach for PDE, multi-dimensional and American Monte Carlo simulation.

Previous Course Code(s): MAFS 6010S

This course is designed for those who are interested in learning from data. It emphasizes the seamless integration of models and algorithms for real applications. Topics include linear methods for regression and classification, tree-based methods, kernel methods, expectation and maximization algorithm, variational auto-encoder, and generative adversarial networks. This course aims to make connections among these topics rather than treating them separately, laying a solid foundation for machine learning and its applications.

Previous Course Code(s): MAFS 6010W

This course teaches basic skills of Python as a programming language, but with a strong focus on using mini-projects with industry backgrounds, so as to help students form good thinking habits in Python when solving practical problems. The first part of the course will be about Python as a programming language, especially on: environment and deployment, data structure and analysis, medium- to large-scale programming. The second part of the course will be mini-projects that help further illustrate best practices and form good habits in Python.

Previous Course Code(s): MAFS 6010Q

Leading financial firms to offer capstone projects involving a combination of quantitative skills (the math/stat or machine learning part) and finance, but the topics are mainly decided by industry supervisors.

Previous Course Code(s): MAFS 6010T

This course is highly similar in instruction to MAFS6010Q but offered in different semesters of the academic year.

Theory of interest rates, yield curves, short rates, forward rates. Short rate models: Vasicek model and Cox-Ingersoll-Ross models. Term structure models: Hull-White fitting procedure. Heath-Jarrow-Morton pricing framework. LIBOR and swap market models

Numerical solution of differential equations, finite difference method, finite element methods, spectral methods and boundary integral methods. Basic theory of convergence, stability and error estimates.

An introduction to reinforcement learning and financial applications. Topics include finite action space and finite state space problem, classical RL algorithms, Q learning, policy gradient methods, and DRL – deep Q learning.