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.

Various 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.

Credit 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.

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.

Primitive data types, objects and classes, funcitons and event-driver programmings in Java and Excel. Applications examples in finance.

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.

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.

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

The course aims to equip students with the knowledge and understanding of China onshore and offshore markets, products and regulations. It also introduces students to the perspectives of various market players, their considerations and how these considerations impact various opportunities for capital raising, investment and FX hedging. Throughout the course, relevant current events and landmark deals in each area are examined and used to illustrate teaching points.

The whole process of financial engineering will be introduced from payoff design/ packaging/ distribution to pricing/ hedging/ funding. The popular and representative structures across the asset classes (Equity, Funds, FX, Interest Rate, Credit and Commodities) will be presented with discussions on the investment rationale, modelling, pricing and hedging techniques. The customized index business based on factors, portfolio theory and other trading models are also introduced with up-to-date industry practices.

This course provides an introduction to the technology of distributed ledger or shared ledger, which is essentially an asset database that can be shared across a network of multiple sites, countries or institutions and achieves secure and valid distributed consensus. A typical design is the blockchain system.  Various financial applications, including bitcoin and other cryptocurrencies, are reviewed.

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.

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

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 programing.

This course introduces modern methodologies in machine learning, including tools in both supervised learning and unsupervised learning. Examples includes linear regression and classification, tree-based methods, kernel methods and principal component analysis.