A foundation course developing the essential mathematical methods for MFM (Master of Financial Mathematics program). The course focuses on the theoretical development of stochastic calculus in continuous time with emphasis on quantitative risk analysis. Topics include: Measure Theory, Brownian Motion, Ito Calculus, Risk-Neutral Pricing, Stochastic Differential Equations, Connections with Partial Differential Equations, Interest Rate Models.
Practical overview of global financial markets and securities with an emphasis on understanding the key roles played by mathematicians and the modeling work they use in pricing, hedging and risk assessment. Practical skills are developed following industry practices and requirements. Topics include: Introduction to Markets, Market Data, Stochastic Models, Equity Options, Hedging, Black-Scholes-Merton model, Greeks, Model Shortcomings, Foreign Exchange Options, Fixed Income Instruments, Value at Risk and other practical Risk Measurement and Management Issues and Techniques.
This course introduces the students to the different types of data routinely produced by financial markets, including stock prices and derivatives prices, order books, and risk factors. Students are expected to become familiar with the computational techniques used to analyze and simulate financial data, as well as implement, calibrate, and validate models, including machine learning and other novel data analytics techniques. These computational methods are essential for practical applications of all concepts introduced in the MFM (Master of Financial Mathematics) program.
Statistical methods in data science with emphasis on financial securities data. Topics include: Sampling Distribution, Point Estimation, Interval Estimation, Linear regression, Financial Time Series, Model Validation and Fitting, Multivariate Models and Dependencies, Signal Processing, Topics in Data Analytics.
Problems solving in portfolio management with financial optimization techniques. Topics include: Portfolio Risk Measurements, Mean Variance Analysis, Mean Value at Risk Analysis, Capital Asset Pricing Model and Portfolio Performance Indices, Optimization in Finance.
This course develops models for defaultable firms and practical methods to value the securities they issue and manage their risk. Topics include: Fixed Income Markets, Structural Firm Default Models, Reduced Form Models, Recovery Modelling, Default Dependence, Portfolio Credit Risk, Counterparty Risk, Credit Value Adjustment and extensions.
Development of numerical methods with emphasis on derivative securities pricing. Topics include: Numerical solutions to PDEs and SDEs, Numerical Methods for Exotic and Path Dependent Options, Free Boundary for American Options.
Modern trends and topics in risk management are studied in course modules that are changed and adapted to follow the current issues and needs in the financial industry. Guest speakers from industry contribute teaching on topics of immediate relevance in practice. Topics include: Credit Risk Capital, Counterparty Risk, Risk in Retail Portfolios, Algorithmic and High Frequency Trading, Financial Technologies, and additional topical issues of capital quantification and risk management as identified by industry partners.
Aims to provide experiential learning through the completion of a major project of current industrial interest. The student will work together with a mentor from a financial institution, or alternatively, may undertake the project while working as an intern in the financial industry. By completing a paper and oral presentation, the student will strengthen the professional skills and experience required to launch a career in the financial industry.