Postgraduate Courses

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.

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.

Data 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.

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.

This 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.

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.

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.

Java 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.

Selected special topics in Financial Mathematics of current interest but not covered by existing courses.

Completion 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.