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Degree Requirements

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Course Structure

Students are required to complete 36 credits, including at least 27 credits from the List of Required Courses (please see details below), and up to 9 credits of free electives/MAFS 6100 Independent Project.

Required Courses

MAFS 5010 : Stochastic Calculus
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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.

MAFS 5020 : Advanced Probability and Statistics
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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

MAFS 5030 : Quantitative Modeling of Derivatives Securities
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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.

MAFS 5040 : Quantitative Methods for Fixed-income Instruments
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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.

MAFS 5110 : Advanced Data Analysis with Statistical Programming
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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.

MAFS 5130 : Quantitative Analysis of Financial Time Series
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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

MAFS 5140 : Statistical Methods in Quantitative Finance
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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.

MAFS 5210 : Mathematical Models of Investment
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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.

MAFS 5220 : Quantitative Risk Management
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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.

MAFS 5240 : Software Development with C++ for Quantitative Finance
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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

MAFS 5250 : Computational Methods for Pricing Structured Products
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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.

MAFS 5270 : Mathematical Market Microstructure
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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.

MAFS 5280 : Financial Markets in Hong Kong and China
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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.

MAFS5310 : Portfolio Optimization with R
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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.

MAFS 5330 : Structured Products - Analysis and Pricing
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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.

MAFS 5340 : Machine Learning and its Applications
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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.

MAFS 5360 : Computing for Finance in Python
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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.

MAFS 5370 : Reinforcement Learning with Financial Applications
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Previous Course Code(s): MAFS 6010Y

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.

MAFS 5380 : Entrepreneurship in Fintech
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Previous Course Code(s): MAFS 6010X

This course will prepare you for your entrepreneurial journey. This class should be of interest to entrepreneurs who want to build innovative companies or employees who want to work for them. Remember that even if you don’t want to build or work for any of these companies, you’ll still need to navigate the world that they’re building.

MAFS 6000 : Capstone Project in Financial Mathematics
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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.

MAFS 6001 : Capstone Project in Financial Mathematics II
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Previous Course Code(s): MAFS 6010T

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

MATH 5520 : Interest Rate Models
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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

MATH 5311 : Advanced Numerical Methods I
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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.

MAFS 6010 — Special Topics in Financial Mathematics (Course Series)
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Note: Courses offered in this series varies year from year. The courses listed in the following may not be exclusive, other courses have been or will be offered.

MAFS 6010Z : Artificial Intelligence in Fintech
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This course explores the basic concepts and underlying principles of AI, delving into the fundamentals of machine learning with insights from case studies of relevant technologies. Allowing for the experimentation of applications of machine learning, this course is designed to encourage students to devise creative ways to put readily-available AI technologies to use to tackle practical Finance problems (e.g., Payment, Credit, Trading, Insurance) in real life.

MAFS 6010A : Decentralized Finance
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This course introduces a brief history of decentralized finance and covers the innovations and breakthroughs since the "DeFi summer" of 2020. We review major projects in stablecoins, decentralized exchanges, lending and borrowing, asset management, farming and mining, insurance and derivatives. The aim of this course is learning to design new and innovative DeFi projects.

MAFS 6010B : Simulation and Optimization in Quantitative Finance
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The course covers Monte Carlo simulation methods (general formulation of simulation procedure; pricing of financial derivatives; variance reduction techniques; simulation of random default times), Rare event simulation in copula risk models (normal copula and t-copula models; exponential twisting methods; cross entropy methods), Quadratic programming and portfolio optimization (formulation of quadratic programming; Black-Litterman model; constructing an index fund), Dynamic and stochastic programming models (backward induction procedure; optimal stopping models; formulation of stochastic programming; asset and liability management ), Expected utility theory (log utility in long term growth; maximum expected utility criterion; risk aversion coefficients; stochastic dominance; prospect theory), and Portfolio choices and investment decisions under utility maximization (utility optimization in portfolio analysis; optimal consumption and investment models; market equilibrium and optimal allocations).

MAFS 6010C: Introduction to Blockchain Technology
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This course introduces basic concepts and technologies of blockchain, such as the hash function and digital signature, as well as the blockchain applications, especially in Fintech. The students will learn the consensus protocols and algorithms, the incentives and politics of the blockchain community, the mechanics of Bitcoin and Bitcoin mining. The course also covers the limitations and possible improvements of the blockchain system.

MAFS 6010D: Financial Innovations in Web 3.0
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The main characteristics of the financial innovations are that they are open, easy-to-access, global and programmable. These innovations are mostly based on the blockchain technology and aim to increase accessibility, efficiency and transparency of financial services. They include decentralized financial services covering lending, borrowing, trading, insurance, etc, and stablecoins, non-fungible tokens (NFTs), asset tokenization, decentralized autonomous organizations (DAOs), digital wallets, identities and web3 payments, etc.

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In addition to the courses listed above, free electives can be (1) MAFS6100 Independent Project (with a maximum of 6 credits), (2) courses offered by Dept of Mathematics (MATH) at 4000-level or above (with a maximum of 6 credits from 4000-level), or (3) other courses outside MATH at 5000-level or above (subject to approval).

Graduation Requirement

Students must complete the program with a graduation grade average (GGA) of 2.850 or above (out of a scale of 4.3) as required of all postgraduate students at the University. For the calculation of grade averages and related University regulations, please refer to the "Course Grading" page from the Handbook for Taught Postgraduate Studies

Detailed curriculum requirements for students admitted in different academic years are published in the Postgraduate Program Catalog.